0.5x^2-15x=100

Solution for 0.5x^2-15x=100 equation:

0.5x^2-15x=100

We move all terms to the left:

0.5x^2-15x-(100)=0

a = 0.5; b = -15; c = -100;
Δ = b2-4ac
Δ = -152-4·0.5·(-100)
Δ = 425
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:

$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5\sqrt{17}}{2*0.5}=\frac{15-5\sqrt{17}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5\sqrt{17}}{2*0.5}=\frac{15+5\sqrt{17}}{1}
$