100=(x+12)(x)

Solution for 100=(x+12)(x) equation:

100=(x+12)(x)

We move all terms to the left:

100-((x+12)(x))=0


We calculate terms in parentheses: -((x+12)x), so:

(x+12)x

We multiply parentheses

x^2+12x

Back to the equation:

-(x^2+12x)


We get rid of parentheses

-x^2-12x+100=0

We add all the numbers together, and all the variables

-1x^2-12x+100=0

a = -1; b = -12; c = +100;
Δ = b2-4ac
Δ = -122-4·(-1)·100
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{34}}{2*-1}=\frac{12-4\sqrt{34}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{34}}{2*-1}=\frac{12+4\sqrt{34}}{-2}
$