(x-12)(2x+25)=0

Solution for (x-12)(2x+25)=0 equation:

(x-12)(2x+25)=0

We multiply parentheses ..

(+2x^2+25x-24x-300)=0

We get rid of parentheses

2x^2+25x-24x-300=0

We add all the numbers together, and all the variables

2x^2+x-300=0

a = 2; b = 1; c = -300;
Δ = b2-4ac
Δ = 12-4·2·(-300)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-49}{2*2}=\frac{-50}{4}
=-12+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+49}{2*2}=\frac{48}{4}
=12
$