4x^2+192=64x

Solution for 4x^2+192=64x equation:

4x^2+192=64x

We move all terms to the left:

4x^2+192-(64x)=0

a = 4; b = -64; c = +192;
Δ = b2-4ac
Δ = -642-4·4·192
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{-(-64)-32}{2*4}=\frac{32}{8}
=4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+32}{2*4}=\frac{96}{8}
=12
$