15x^2+10x-12=0

Solution for 15x^2+10x-12=0 equation:

15x^2+10x-12=0

a = 15; b = 10; c = -12;
Δ = b2-4ac
Δ = 102-4·15·(-12)
Δ = 820
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:

$\sqrt{\Delta}=\sqrt{820}=\sqrt{4*205}=\sqrt{4}*\sqrt{205}=2\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{205}}{2*15}=\frac{-10-2\sqrt{205}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{205}}{2*15}=\frac{-10+2\sqrt{205}}{30}
$