(x+4)*(2x-7)=108

Solution for (x+4)*(2x-7)=108 equation:

(x+4)(2x-7)=108

We move all terms to the left:

(x+4)(2x-7)-(108)=0

We multiply parentheses ..

(+2x^2-7x+8x-28)-108=0

We get rid of parentheses

2x^2-7x+8x-28-108=0

We add all the numbers together, and all the variables

2x^2+x-136=0

a = 2; b = 1; c = -136;
Δ = b2-4ac
Δ = 12-4·2·(-136)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-33}{2*2}=\frac{-34}{4}
=-8+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+33}{2*2}=\frac{32}{4}
=8
$