(3x-12)(10-5x)=0

Solution for (3x-12)(10-5x)=0 equation:

(3x-12)(10-5x)=0

We add all the numbers together, and all the variables

(3x-12)(-5x+10)=0

We multiply parentheses ..

(-15x^2+30x+60x-120)=0

We get rid of parentheses

-15x^2+30x+60x-120=0

We add all the numbers together, and all the variables

-15x^2+90x-120=0

a = -15; b = 90; c = -120;
Δ = b2-4ac
Δ = 902-4·(-15)·(-120)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-30}{2*-15}=\frac{-120}{-30}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+30}{2*-15}=\frac{-60}{-30}
=+2
$