16=-0.5x^2+25x-150.5

Solution for 16=-0.5x^2+25x-150.5 equation:

16=-0.5x^2+25x-150.5

We move all terms to the left:

16-(-0.5x^2+25x-150.5)=0

We get rid of parentheses

0.5x^2-25x+150.5+16=0

We add all the numbers together, and all the variables

0.5x^2-25x+166.5=0

a = 0.5; b = -25; c = +166.5;
Δ = b2-4ac
Δ = -252-4·0.5·166.5
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-2\sqrt{73}}{2*0.5}=\frac{25-2\sqrt{73}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+2\sqrt{73}}{2*0.5}=\frac{25+2\sqrt{73}}{1}
$