(2x-6)(7x-7)=112

Solution for (2x-6)(7x-7)=112 equation:

(2x-6)(7x-7)=112

We move all terms to the left:

(2x-6)(7x-7)-(112)=0

We multiply parentheses ..

(+14x^2-14x-42x+42)-112=0

We get rid of parentheses

14x^2-14x-42x+42-112=0

We add all the numbers together, and all the variables

14x^2-56x-70=0

a = 14; b = -56; c = -70;
Δ = b2-4ac
Δ = -562-4·14·(-70)
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-84}{2*14}=\frac{-28}{28}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+84}{2*14}=\frac{140}{28}
=5
$