6(2x+3)(5x-1)=0

Solution for 6(2x+3)(5x-1)=0 equation:

6(2x+3)(5x-1)=0

We multiply parentheses ..

6(+10x^2-2x+15x-3)=0

We multiply parentheses

60x^2-12x+90x-18=0

We add all the numbers together, and all the variables

60x^2+78x-18=0

a = 60; b = 78; c = -18;
Δ = b2-4ac
Δ = 782-4·60·(-18)
Δ = 10404
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10404}=102$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-102}{2*60}=\frac{-180}{120}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+102}{2*60}=\frac{24}{120}
=1/5
$