189^2=x(x+12)

Solution for 189^2=x(x+12) equation:

189^2=x(x+12)

We move all terms to the left:

189^2-(x(x+12))=0

We add all the numbers together, and all the variables

-(x(x+12))+35721=0


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

x(x+12)

We multiply parentheses

x^2+12x

Back to the equation:

-(x^2+12x)


We get rid of parentheses

-x^2-12x+35721=0

We add all the numbers together, and all the variables

-1x^2-12x+35721=0

a = -1; b = -12; c = +35721;
Δ = b2-4ac
Δ = -122-4·(-1)·35721
Δ = 143028
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:

$\sqrt{\Delta}=\sqrt{143028}=\sqrt{36*3973}=\sqrt{36}*\sqrt{3973}=6\sqrt{3973}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{3973}}{2*-1}=\frac{12-6\sqrt{3973}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{3973}}{2*-1}=\frac{12+6\sqrt{3973}}{-2}
$