48x-16x^2=10

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

48x-16x^2=10

We move all terms to the left:

48x-16x^2-(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}
$