(12x-9)(4x+10)=0

Solution for (12x-9)(4x+10)=0 equation:

(12x-9)(4x+10)=0

We multiply parentheses ..

(+48x^2+120x-36x-90)=0

We get rid of parentheses

48x^2+120x-36x-90=0

We add all the numbers together, and all the variables

48x^2+84x-90=0

a = 48; b = 84; c = -90;
Δ = b2-4ac
Δ = 842-4·48·(-90)
Δ = 24336
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{24336}=156$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-156}{2*48}=\frac{-240}{96}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+156}{2*48}=\frac{72}{96}
=3/4
$