4x^2+24x=39

Solution for 4x^2+24x=39 equation:

4x^2+24x=39

We move all terms to the left:

4x^2+24x-(39)=0

a = 4; b = 24; c = -39;
Δ = b2-4ac
Δ = 242-4·4·(-39)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-20\sqrt{3}}{2*4}=\frac{-24-20\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+20\sqrt{3}}{2*4}=\frac{-24+20\sqrt{3}}{8}
$