64x-16x^2+48=-48

Solution for 64x-16x^2+48=-48 equation:

64x-16x^2+48=-48

We move all terms to the left:

64x-16x^2+48-(-48)=0

We add all the numbers together, and all the variables

-16x^2+64x+96=0

a = -16; b = 64; c = +96;
Δ = b2-4ac
Δ = 642-4·(-16)·96
Δ = 10240
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:

$\sqrt{\Delta}=\sqrt{10240}=\sqrt{1024*10}=\sqrt{1024}*\sqrt{10}=32\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-32\sqrt{10}}{2*-16}=\frac{-64-32\sqrt{10}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+32\sqrt{10}}{2*-16}=\frac{-64+32\sqrt{10}}{-32}
$