4x^2+24x=9

Solution for 4x^2+24x=9 equation:

4x^2+24x=9

We move all terms to the left:

4x^2+24x-(9)=0

a = 4; b = 24; c = -9;
Δ = b2-4ac
Δ = 242-4·4·(-9)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12\sqrt{5}}{2*4}=\frac{-24-12\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12\sqrt{5}}{2*4}=\frac{-24+12\sqrt{5}}{8}
$