Find three consecutive even integers such that the first plus twice the second plus four times the third equals 174

unknown values: 2*k,2*k+2,2*k+4

equation: 2*k+2*(2*k+2)+4*(2*k+4)=174

answer: 22;24;26

find three consecutive numbers such that twice the square of the first number is 38 more than the product of the other two numbers.

unknown values: x,x+1,x+2

equation: 2*x^2 = (x+1)(x+2) + 38

answer: 8;9;10 or -5;-4;-3

Three times the square of a certain positive number exceeds six times the number by nine. Find the number:

unknown values: x

equation: 3*x^2-6*x=9

answer: 3

Find the whole number such that twice its square is 11 more than 21 times the original number ?

unknown values: x

equation: 2*x^2 = 21*x + 11

answer: 11

three times the square of a certain positive number exceeds six times the number by nine. Find the number.

unknown values: n

equation: 3*n^2 = 6*n + 9

answer: 3

the product of some negative number and 5 less than twice that number is 493. find the number?

unknown values: x

equation: x(2*x - 5) = 493

equation: x

< 0 answer: -14.5 The sum of the digits of a two-digit number is 7. If the digits are reversed, the new number is increased by 3 equals 4 times the original number. what is the number? unknown values: n equation: n = 10*x+y equation: x+y=7 equation: 4*(10*x+y)=10*y+x+3 answer: 16 When one half of the second of two consecutive integers is subtracted from the first of the two consecutive integers, the result is 2. what is the first number? unknown values: x equation: x-(x+1)/2=2 answer: 5 twice the larger of two numbers is three more than five times the smaller and the sum of four times the larger and three times the smaller is 71. What are the numbers? unknown values: x,y equation: 2*x = 5*y+3 equation: 4*x+3*y = 71 answer: {14;5} find two numbers such that five times the larger plus three times the smaller is 47 and four times the larger minus twice the smaller is 20. unknown values: x,y equation: 5*y+3*x=47 equation: 4*y-2*x=20 answer: {4; 7}