-30x^2-52x+20=0

Solution for -30x^2-52x+20=0 equation:

-30x^2-52x+20=0

a = -30; b = -52; c = +20;
Δ = b2-4ac
Δ = -522-4·(-30)·20
Δ = 5104
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:

$\sqrt{\Delta}=\sqrt{5104}=\sqrt{16*319}=\sqrt{16}*\sqrt{319}=4\sqrt{319}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-4\sqrt{319}}{2*-30}=\frac{52-4\sqrt{319}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+4\sqrt{319}}{2*-30}=\frac{52+4\sqrt{319}}{-60}
$