(2x-5)(x-4)=12

Solution for (2x-5)(x-4)=12 equation:

(2x-5)(x-4)=12

We move all terms to the left:

(2x-5)(x-4)-(12)=0

We multiply parentheses ..

(+2x^2-8x-5x+20)-12=0

We get rid of parentheses

2x^2-8x-5x+20-12=0

We add all the numbers together, and all the variables

2x^2-13x+8=0

a = 2; b = -13; c = +8;
Δ = b2-4ac
Δ = -132-4·2·8
Δ = 105
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{-(-13)-\sqrt{105}}{2*2}=\frac{13-\sqrt{105}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{105}}{2*2}=\frac{13+\sqrt{105}}{4}
$