9*2^2x=576

Solution for 9*2^2x=576 equation:

9*2^2x=576

We move all terms to the left:

9*2^2x-(576)=0

Wy multiply elements

18x^2-576=0

a = 18; b = 0; c = -576;
Δ = b2-4ac
Δ = 02-4·18·(-576)
Δ = 41472
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:

$\sqrt{\Delta}=\sqrt{41472}=\sqrt{20736*2}=\sqrt{20736}*\sqrt{2}=144\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-144\sqrt{2}}{2*18}=\frac{0-144\sqrt{2}}{36}
=-\frac{144\sqrt{2}}{36}
=-4\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+144\sqrt{2}}{2*18}=\frac{0+144\sqrt{2}}{36}
=\frac{144\sqrt{2}}{36}
=4\sqrt{2}
$