30x^2-15x-6=0

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

30x^2-15x-6=0

a = 30; b = -15; c = -6;
Δ = b2-4ac
Δ = -152-4·30·(-6)
Δ = 945
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:

$\sqrt{\Delta}=\sqrt{945}=\sqrt{9*105}=\sqrt{9}*\sqrt{105}=3\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{105}}{2*30}=\frac{15-3\sqrt{105}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{105}}{2*30}=\frac{15+3\sqrt{105}}{60}
$