(2x-6)(x-7)=7

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

(2x-6)(x-7)=7

We move all terms to the left:

(2x-6)(x-7)-(7)=0

We multiply parentheses ..

(+2x^2-14x-6x+42)-7=0

We get rid of parentheses

2x^2-14x-6x+42-7=0

We add all the numbers together, and all the variables

2x^2-20x+35=0

a = 2; b = -20; c = +35;
Δ = b2-4ac
Δ = -202-4·2·35
Δ = 120
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{30}}{2*2}=\frac{20-2\sqrt{30}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{30}}{2*2}=\frac{20+2\sqrt{30}}{4}
$