125=0.5x^2+25x-150

Solution for 125=0.5x^2+25x-150 equation:

125=0.5x^2+25x-150

We move all terms to the left:

125-(0.5x^2+25x-150)=0

We get rid of parentheses

-0.5x^2-25x+150+125=0

We add all the numbers together, and all the variables

-0.5x^2-25x+275=0

a = -0.5; b = -25; c = +275;
Δ = b2-4ac
Δ = -252-4·(-0.5)·275
Δ = 1175
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:

$\sqrt{\Delta}=\sqrt{1175}=\sqrt{25*47}=\sqrt{25}*\sqrt{47}=5\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-5\sqrt{47}}{2*-0.5}=\frac{25-5\sqrt{47}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+5\sqrt{47}}{2*-0.5}=\frac{25+5\sqrt{47}}{-1}
$