9x^2-4x=192

Solution for 9x^2-4x=192 equation:

9x^2-4x=192

We move all terms to the left:

9x^2-4x-(192)=0

a = 9; b = -4; c = -192;
Δ = b2-4ac
Δ = -42-4·9·(-192)
Δ = 6928
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:

$\sqrt{\Delta}=\sqrt{6928}=\sqrt{16*433}=\sqrt{16}*\sqrt{433}=4\sqrt{433}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{433}}{2*9}=\frac{4-4\sqrt{433}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{433}}{2*9}=\frac{4+4\sqrt{433}}{18}
$