-3x^2=54x+240

Solution for -3x^2=54x+240 equation:

-3x^2=54x+240

We move all terms to the left:

-3x^2-(54x+240)=0

We get rid of parentheses

-3x^2-54x-240=0

a = -3; b = -54; c = -240;
Δ = b2-4ac
Δ = -542-4·(-3)·(-240)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6}{2*-3}=\frac{48}{-6}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6}{2*-3}=\frac{60}{-6}
=-10
$