3x2-90x+24=0

Solution for 3x2-90x+24=0 equation:

3x^2-90x+24=0

a = 3; b = -90; c = +24;
Δ = b2-4ac
Δ = -902-4·3·24
Δ = 7812
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:

$\sqrt{\Delta}=\sqrt{7812}=\sqrt{36*217}=\sqrt{36}*\sqrt{217}=6\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-6\sqrt{217}}{2*3}=\frac{90-6\sqrt{217}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+6\sqrt{217}}{2*3}=\frac{90+6\sqrt{217}}{6}
$