15x2+3x-6=0

Solution for 15x2+3x-6=0 equation:

15x^2+3x-6=0

a = 15; b = 3; c = -6;
Δ = b2-4ac
Δ = 32-4·15·(-6)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{41}}{2*15}=\frac{-3-3\sqrt{41}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{41}}{2*15}=\frac{-3+3\sqrt{41}}{30}
$