48x^2-96x+32=0

Solution for 48x^2-96x+32=0 equation:

48x^2-96x+32=0

a = 48; b = -96; c = +32;
Δ = b2-4ac
Δ = -962-4·48·32
Δ = 3072
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:

$\sqrt{\Delta}=\sqrt{3072}=\sqrt{1024*3}=\sqrt{1024}*\sqrt{3}=32\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-32\sqrt{3}}{2*48}=\frac{96-32\sqrt{3}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+32\sqrt{3}}{2*48}=\frac{96+32\sqrt{3}}{96}
$