-8x^2+48x+58=0

Solution for -8x^2+48x+58=0 equation:

-8x^2+48x+58=0

a = -8; b = 48; c = +58;
Δ = b2-4ac
Δ = 482-4·(-8)·58
Δ = 4160
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:

$\sqrt{\Delta}=\sqrt{4160}=\sqrt{64*65}=\sqrt{64}*\sqrt{65}=8\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-8\sqrt{65}}{2*-8}=\frac{-48-8\sqrt{65}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+8\sqrt{65}}{2*-8}=\frac{-48+8\sqrt{65}}{-16}
$