(x-2)(x+9)=12

Solution for (x-2)(x+9)=12 equation:

(x-2)(x+9)=12

We move all terms to the left:

(x-2)(x+9)-(12)=0

We multiply parentheses ..

(+x^2+9x-2x-18)-12=0

We get rid of parentheses

x^2+9x-2x-18-12=0

We add all the numbers together, and all the variables

x^2+7x-30=0

a = 1; b = 7; c = -30;
Δ = b2-4ac
Δ = 72-4·1·(-30)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-13}{2*1}=\frac{-20}{2}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+13}{2*1}=\frac{6}{2}
=3
$