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

Solution for 0=-0.5x^2+25x-225 equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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}
$