6x^2+30x=450

Solution for 6x^2+30x=450 equation:

6x^2+30x=450

We move all terms to the left:

6x^2+30x-(450)=0

a = 6; b = 30; c = -450;
Δ = b2-4ac
Δ = 302-4·6·(-450)
Δ = 11700
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:

$\sqrt{\Delta}=\sqrt{11700}=\sqrt{900*13}=\sqrt{900}*\sqrt{13}=30\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30\sqrt{13}}{2*6}=\frac{-30-30\sqrt{13}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30\sqrt{13}}{2*6}=\frac{-30+30\sqrt{13}}{12}
$