3x^2+30x=240

Solution for 3x^2+30x=240 equation:

3x^2+30x=240

We move all terms to the left:

3x^2+30x-(240)=0

a = 3; b = 30; c = -240;
Δ = b2-4ac
Δ = 302-4·3·(-240)
Δ = 3780
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:

$\sqrt{\Delta}=\sqrt{3780}=\sqrt{36*105}=\sqrt{36}*\sqrt{105}=6\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{105}}{2*3}=\frac{-30-6\sqrt{105}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{105}}{2*3}=\frac{-30+6\sqrt{105}}{6}
$