(2x-12)(x-7)=60

Solution for (2x-12)(x-7)=60 equation:

(2x-12)(x-7)=60

We move all terms to the left:

(2x-12)(x-7)-(60)=0

We multiply parentheses ..

(+2x^2-14x-12x+84)-60=0

We get rid of parentheses

2x^2-14x-12x+84-60=0

We add all the numbers together, and all the variables

2x^2-26x+24=0

a = 2; b = -26; c = +24;
Δ = b2-4ac
Δ = -262-4·2·24
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-22}{2*2}=\frac{4}{4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+22}{2*2}=\frac{48}{4}
=12
$