-0.5x^2+25x-108=117

Solution for -0.5x^2+25x-108=117 equation:

-0.5x^2+25x-108=117

We move all terms to the left:

-0.5x^2+25x-108-(117)=0

We add all the numbers together, and all the variables

-0.5x^2+25x-225=0

a = -0.5; b = 25; c = -225;
Δ = b2-4ac
Δ = 252-4·(-0.5)·(-225)
Δ = 175
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:

$\sqrt{\Delta}=\sqrt{175}=\sqrt{25*7}=\sqrt{25}*\sqrt{7}=5\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-5\sqrt{7}}{2*-0.5}=\frac{-25-5\sqrt{7}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+5\sqrt{7}}{2*-0.5}=\frac{-25+5\sqrt{7}}{-1}
$