(2x+7)(x-6)=4x+14

Solution for (2x+7)(x-6)=4x+14 equation:

(2x+7)(x-6)=4x+14

We move all terms to the left:

(2x+7)(x-6)-(4x+14)=0

We get rid of parentheses

(2x+7)(x-6)-4x-14=0

We multiply parentheses ..

(+2x^2-12x+7x-42)-4x-14=0

We get rid of parentheses

2x^2-12x+7x-4x-42-14=0

We add all the numbers together, and all the variables

2x^2-9x-56=0

a = 2; b = -9; c = -56;
Δ = b2-4ac
Δ = -92-4·2·(-56)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-23}{2*2}=\frac{-14}{4}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+23}{2*2}=\frac{32}{4}
=8
$