-6(x-5)(3x+4)=0

Solution for -6(x-5)(3x+4)=0 equation:

-6(x-5)(3x+4)=0

We multiply parentheses ..

-6(+3x^2+4x-15x-20)=0

We multiply parentheses

-18x^2-24x+90x+120=0

We add all the numbers together, and all the variables

-18x^2+66x+120=0

a = -18; b = 66; c = +120;
Δ = b2-4ac
Δ = 662-4·(-18)·120
Δ = 12996
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12996}=114$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-114}{2*-18}=\frac{-180}{-36}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+114}{2*-18}=\frac{48}{-36}
=-1+1/3
$