(x-12)(x+3)=364

Solution for (x-12)(x+3)=364 equation:

(x-12)(x+3)=364

We move all terms to the left:

(x-12)(x+3)-(364)=0

We multiply parentheses ..

(+x^2+3x-12x-36)-364=0

We get rid of parentheses

x^2+3x-12x-36-364=0

We add all the numbers together, and all the variables

x^2-9x-400=0

a = 1; b = -9; c = -400;
Δ = b2-4ac
Δ = -92-4·1·(-400)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-41}{2*1}=\frac{-32}{2}
=-16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+41}{2*1}=\frac{50}{2}
=25
$