48x-64x^2=-9

Solution for 48x-64x^2=-9 equation:

48x-64x^2=-9

We move all terms to the left:

48x-64x^2-(-9)=0

We add all the numbers together, and all the variables

-64x^2+48x+9=0

a = -64; b = 48; c = +9;
Δ = b2-4ac
Δ = 482-4·(-64)·9
Δ = 4608
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:

$\sqrt{\Delta}=\sqrt{4608}=\sqrt{2304*2}=\sqrt{2304}*\sqrt{2}=48\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-48\sqrt{2}}{2*-64}=\frac{-48-48\sqrt{2}}{-128}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+48\sqrt{2}}{2*-64}=\frac{-48+48\sqrt{2}}{-128}
$