-6x^2+30x+72=0

Solution for -6x^2+30x+72=0 equation:

-6x^2+30x+72=0

a = -6; b = 30; c = +72;
Δ = b2-4ac
Δ = 302-4·(-6)·72
Δ = 2628
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:

$\sqrt{\Delta}=\sqrt{2628}=\sqrt{36*73}=\sqrt{36}*\sqrt{73}=6\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{73}}{2*-6}=\frac{-30-6\sqrt{73}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{73}}{2*-6}=\frac{-30+6\sqrt{73}}{-12}
$