5x^2=48x-64

Solution for 5x^2=48x-64 equation:

5x^2=48x-64

We move all terms to the left:

5x^2-(48x-64)=0

We get rid of parentheses

5x^2-48x+64=0

a = 5; b = -48; c = +64;
Δ = b2-4ac
Δ = -482-4·5·64
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-32}{2*5}=\frac{16}{10}
=1+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+32}{2*5}=\frac{80}{10}
=8
$