24x^2+15x-6=0

Solution for 24x^2+15x-6=0 equation:

24x^2+15x-6=0

a = 24; b = 15; c = -6;
Δ = b2-4ac
Δ = 152-4·24·(-6)
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{89}}{2*24}=\frac{-15-3\sqrt{89}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{89}}{2*24}=\frac{-15+3\sqrt{89}}{48}
$