15x^2-2x-12=0

Solution for 15x^2-2x-12=0 equation:

15x^2-2x-12=0

a = 15; b = -2; c = -12;
Δ = b2-4ac
Δ = -22-4·15·(-12)
Δ = 724
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:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{181}}{2*15}=\frac{2-2\sqrt{181}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{181}}{2*15}=\frac{2+2\sqrt{181}}{30}
$