6(2x-3)(10x+5)=0

Solution for 6(2x-3)(10x+5)=0 equation:

6(2x-3)(10x+5)=0

We multiply parentheses ..

6(+20x^2+10x-30x-15)=0

We multiply parentheses

120x^2+60x-180x-90=0

We add all the numbers together, and all the variables

120x^2-120x-90=0

a = 120; b = -120; c = -90;
Δ = b2-4ac
Δ = -1202-4·120·(-90)
Δ = 57600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{57600}=240$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-240}{2*120}=\frac{-120}{240}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+240}{2*120}=\frac{360}{240}
=1+1/2
$