10=48x-16x^2

Solution for 10=48x-16x^2 equation:

10=48x-16x^2

We move all terms to the left:

10-(48x-16x^2)=0

We get rid of parentheses

16x^2-48x+10=0

a = 16; b = -48; c = +10;
Δ = b2-4ac
Δ = -482-4·16·10
Δ = 1664
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:

$\sqrt{\Delta}=\sqrt{1664}=\sqrt{64*26}=\sqrt{64}*\sqrt{26}=8\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{26}}{2*16}=\frac{48-8\sqrt{26}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{26}}{2*16}=\frac{48+8\sqrt{26}}{32}
$