(x-2)(x+1)=12

Solution for (x-2)(x+1)=12 equation:

(x-2)(x+1)=12

We move all terms to the left:

(x-2)(x+1)-(12)=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2-1x-14=0

a = 1; b = -1; c = -14;
Δ = b2-4ac
Δ = -12-4·1·(-14)
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{57}}{2*1}=\frac{1-\sqrt{57}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{57}}{2*1}=\frac{1+\sqrt{57}}{2}
$