6(2x^2-15x-30)=0

Solution for 6(2x^2-15x-30)=0 equation:

6(2x^2-15x-30)=0

We multiply parentheses

12x^2-90x-180=0

a = 12; b = -90; c = -180;
Δ = b2-4ac
Δ = -902-4·12·(-180)
Δ = 16740
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{16740}=\sqrt{36*465}=\sqrt{36}*\sqrt{465}=6\sqrt{465}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-6\sqrt{465}}{2*12}=\frac{90-6\sqrt{465}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+6\sqrt{465}}{2*12}=\frac{90+6\sqrt{465}}{24}
$