108=(x-5)(x-7)

Solution for 108=(x-5)(x-7) equation:

108=(x-5)(x-7)

We move all terms to the left:

108-((x-5)(x-7))=0

We multiply parentheses ..

-((+x^2-7x-5x+35))+108=0


We calculate terms in parentheses: -((+x^2-7x-5x+35)), so:

(+x^2-7x-5x+35)

We get rid of parentheses

x^2-7x-5x+35

We add all the numbers together, and all the variables

x^2-12x+35

Back to the equation:

-(x^2-12x+35)


We get rid of parentheses

-x^2+12x-35+108=0

We add all the numbers together, and all the variables

-1x^2+12x+73=0

a = -1; b = 12; c = +73;
Δ = b2-4ac
Δ = 122-4·(-1)·73
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{109}}{2*-1}=\frac{-12-2\sqrt{109}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{109}}{2*-1}=\frac{-12+2\sqrt{109}}{-2}
$