-2x^2+45x+100=0

Solution for -2x^2+45x+100=0 equation:

-2x^2+45x+100=0

a = -2; b = 45; c = +100;
Δ = b2-4ac
Δ = 452-4·(-2)·100
Δ = 2825
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:

$\sqrt{\Delta}=\sqrt{2825}=\sqrt{25*113}=\sqrt{25}*\sqrt{113}=5\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-5\sqrt{113}}{2*-2}=\frac{-45-5\sqrt{113}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+5\sqrt{113}}{2*-2}=\frac{-45+5\sqrt{113}}{-4}
$