6x2+24x-75=0

Solution for 6x2+24x-75=0 equation:

6x^2+24x-75=0

a = 6; b = 24; c = -75;
Δ = b2-4ac
Δ = 242-4·6·(-75)
Δ = 2376
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:

$\sqrt{\Delta}=\sqrt{2376}=\sqrt{36*66}=\sqrt{36}*\sqrt{66}=6\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6\sqrt{66}}{2*6}=\frac{-24-6\sqrt{66}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6\sqrt{66}}{2*6}=\frac{-24+6\sqrt{66}}{12}
$