30=(x-8)*(x-12)

Solution for 30=(x-8)*(x-12) equation:

30=(x-8)(x-12)

We move all terms to the left:

30-((x-8)(x-12))=0

We multiply parentheses ..

-((+x^2-12x-8x+96))+30=0


We calculate terms in parentheses: -((+x^2-12x-8x+96)), so:

(+x^2-12x-8x+96)

We get rid of parentheses

x^2-12x-8x+96

We add all the numbers together, and all the variables

x^2-20x+96

Back to the equation:

-(x^2-20x+96)


We get rid of parentheses

-x^2+20x-96+30=0

We add all the numbers together, and all the variables

-1x^2+20x-66=0

a = -1; b = 20; c = -66;
Δ = b2-4ac
Δ = 202-4·(-1)·(-66)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{34}}{2*-1}=\frac{-20-2\sqrt{34}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{34}}{2*-1}=\frac{-20+2\sqrt{34}}{-2}
$