270=6x^2+24x

Solution for 270=6x^2+24x equation:

270=6x^2+24x

We move all terms to the left:

270-(6x^2+24x)=0

We get rid of parentheses

-6x^2-24x+270=0

a = -6; b = -24; c = +270;
Δ = b2-4ac
Δ = -242-4·(-6)·270
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-84}{2*-6}=\frac{-60}{-12}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+84}{2*-6}=\frac{108}{-12}
=-9
$