24x^2+16=116x

Solution for 24x^2+16=116x equation:

24x^2+16=116x

We move all terms to the left:

24x^2+16-(116x)=0

a = 24; b = -116; c = +16;
Δ = b2-4ac
Δ = -1162-4·24·16
Δ = 11920
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:

$\sqrt{\Delta}=\sqrt{11920}=\sqrt{16*745}=\sqrt{16}*\sqrt{745}=4\sqrt{745}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-116)-4\sqrt{745}}{2*24}=\frac{116-4\sqrt{745}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-116)+4\sqrt{745}}{2*24}=\frac{116+4\sqrt{745}}{48}
$