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

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

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

We multiply parentheses ..

6(+10x^2-6x+25x-15)=0

We multiply parentheses

60x^2-36x+150x-90=0

We add all the numbers together, and all the variables

60x^2+114x-90=0

a = 60; b = 114; c = -90;
Δ = b2-4ac
Δ = 1142-4·60·(-90)
Δ = 34596
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{34596}=186$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(114)-186}{2*60}=\frac{-300}{120}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(114)+186}{2*60}=\frac{72}{120}
=3/5
$