Question

Solve. 6x2 + 8x = 14

Answer 1

6x^2 + 8x = 14
=> 3x^2 + 4x = 7
=> 3x^2 + 4x - 7 = 0

Solve it using quadratic formula

Answer 2

You can also solve it by factorization. \(3x^2+4x-7=(3x+7)(x-1)=0 \implies x=\frac{-7}{3}\) or \(x= 1\).

Answer 3

Possible intermediate steps:
6 x^2+8 x = 14
Divide both sides by 6:
x^2+(4 x)/3 = 7/3
Add 4/9 to both sides:
x^2+(4 x)/3+4/9 = 25/9
Factor the left hand side:
(x+2/3)^2 = 25/9
Take the square root of both sides:
abs(x+2/3) = 5/3
Eliminate the absolute value:
x+2/3 = -5/3 or x+2/3 = 5/3
Subtract 2/3 from both sides:
x = -7/3 or x+2/3 = 5/3
Subtract 2/3 from both sides:
x = -7/3 or x = 1