-16x^2=48x+25

Solution for -16x^2=48x+25 equation:

-16x^2=48x+25

We move all terms to the left:

-16x^2-(48x+25)=0

We get rid of parentheses

-16x^2-48x-25=0

a = -16; b = -48; c = -25;
Δ = b2-4ac
Δ = -482-4·(-16)·(-25)
Δ = 704
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:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{11}}{2*-16}=\frac{48-8\sqrt{11}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{11}}{2*-16}=\frac{48+8\sqrt{11}}{-32}
$