-5x^2+22x+82=0

Solution for -5x^2+22x+82=0 equation:

-5x^2+22x+82=0

a = -5; b = 22; c = +82;
Δ = b2-4ac
Δ = 222-4·(-5)·82
Δ = 2124
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:

$\sqrt{\Delta}=\sqrt{2124}=\sqrt{36*59}=\sqrt{36}*\sqrt{59}=6\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-6\sqrt{59}}{2*-5}=\frac{-22-6\sqrt{59}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+6\sqrt{59}}{2*-5}=\frac{-22+6\sqrt{59}}{-10}
$