3x^2=63x-240

Solution for 3x^2=63x-240 equation:

3x^2=63x-240

We move all terms to the left:

3x^2-(63x-240)=0

We get rid of parentheses

3x^2-63x+240=0

a = 3; b = -63; c = +240;
Δ = b2-4ac
Δ = -632-4·3·240
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-33}{2*3}=\frac{30}{6}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+33}{2*3}=\frac{96}{6}
=16
$