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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-15x-80=0

a = 2; b = -15; c = -80;
Δ = b2-4ac
Δ = -152-4·2·(-80)
Δ = 865
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{865}}{2*2}=\frac{15-\sqrt{865}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{865}}{2*2}=\frac{15+\sqrt{865}}{4}
$