-6x^2+3x+90=0

Solution for -6x^2+3x+90=0 equation:

-6x^2+3x+90=0

a = -6; b = 3; c = +90;
Δ = b2-4ac
Δ = 32-4·(-6)·90
Δ = 2169
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:

$\sqrt{\Delta}=\sqrt{2169}=\sqrt{9*241}=\sqrt{9}*\sqrt{241}=3\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{241}}{2*-6}=\frac{-3-3\sqrt{241}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{241}}{2*-6}=\frac{-3+3\sqrt{241}}{-12}
$