(3x^2)-24x=9

Solution for (3x^2)-24x=9 equation:

(3x^2)-24x=9

We move all terms to the left:

(3x^2)-24x-(9)=0

a = 3; b = -24; c = -9;
Δ = b2-4ac
Δ = -242-4·3·(-9)
Δ = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{19}}{2*3}=\frac{24-6\sqrt{19}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{19}}{2*3}=\frac{24+6\sqrt{19}}{6}
$