6x^2+30x=576

Solution for 6x^2+30x=576 equation:

6x^2+30x=576

We move all terms to the left:

6x^2+30x-(576)=0

a = 6; b = 30; c = -576;
Δ = b2-4ac
Δ = 302-4·6·(-576)
Δ = 14724
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:

$\sqrt{\Delta}=\sqrt{14724}=\sqrt{36*409}=\sqrt{36}*\sqrt{409}=6\sqrt{409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{409}}{2*6}=\frac{-30-6\sqrt{409}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{409}}{2*6}=\frac{-30+6\sqrt{409}}{12}
$