9x2+24x=16

Solution for 9x2+24x=16 equation:

9x^2+24x=16

We move all terms to the left:

9x^2+24x-(16)=0

a = 9; b = 24; c = -16;
Δ = b2-4ac
Δ = 242-4·9·(-16)
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24\sqrt{2}}{2*9}=\frac{-24-24\sqrt{2}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24\sqrt{2}}{2*9}=\frac{-24+24\sqrt{2}}{18}
$