64x^2=48x+9=

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

64x^2=48x+9=

We move all terms to the left:

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

We get rid of parentheses

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}
$