124=-0.5x2+25x-151

Solution for 124=-0.5x2+25x-151 equation:

124=-0.5x^2+25x-151

We move all terms to the left:

124-(-0.5x^2+25x-151)=0

We get rid of parentheses

0.5x^2-25x+151+124=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 = 75
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:

$\sqrt{\Delta}=\sqrt{75}=\sqrt{25*3}=\sqrt{25}*\sqrt{3}=5\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-5\sqrt{3}}{2*0.5}=\frac{25-5\sqrt{3}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+5\sqrt{3}}{2*0.5}=\frac{25+5\sqrt{3}}{1}
$