-6(2x+3)(x-20)=0

Solution for -6(2x+3)(x-20)=0 equation:

-6(2x+3)(x-20)=0

We multiply parentheses ..

-6(+2x^2-40x+3x-60)=0

We multiply parentheses

-12x^2+240x-18x+360=0

We add all the numbers together, and all the variables

-12x^2+222x+360=0

a = -12; b = 222; c = +360;
Δ = b2-4ac
Δ = 2222-4·(-12)·360
Δ = 66564
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{66564}=258$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(222)-258}{2*-12}=\frac{-480}{-24}
=+20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(222)+258}{2*-12}=\frac{36}{-24}
=-1+1/2
$