48x-16x^2=28

Solution for 48x-16x^2=28 equation:

48x-16x^2=28

We move all terms to the left:

48x-16x^2-(28)=0

a = -16; b = 48; c = -28;
Δ = b2-4ac
Δ = 482-4·(-16)·(-28)
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-16\sqrt{2}}{2*-16}=\frac{-48-16\sqrt{2}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+16\sqrt{2}}{2*-16}=\frac{-48+16\sqrt{2}}{-32}
$