(x-12)(x+35)=0

Solution for (x-12)(x+35)=0 equation:

(x-12)(x+35)=0

We multiply parentheses ..

(+x^2+35x-12x-420)=0

We get rid of parentheses

x^2+35x-12x-420=0

We add all the numbers together, and all the variables

x^2+23x-420=0

a = 1; b = 23; c = -420;
Δ = b2-4ac
Δ = 232-4·1·(-420)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-47}{2*1}=\frac{-70}{2}
=-35
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+47}{2*1}=\frac{24}{2}
=12
$