16x^2-9x=576

Solution for 16x^2-9x=576 equation:

16x^2-9x=576

We move all terms to the left:

16x^2-9x-(576)=0

a = 16; b = -9; c = -576;
Δ = b2-4ac
Δ = -92-4·16·(-576)
Δ = 36945
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:

$\sqrt{\Delta}=\sqrt{36945}=\sqrt{9*4105}=\sqrt{9}*\sqrt{4105}=3\sqrt{4105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{4105}}{2*16}=\frac{9-3\sqrt{4105}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{4105}}{2*16}=\frac{9+3\sqrt{4105}}{32}
$