15x-0.5*x^2-100=0

Solution for 15x-0.5*x^2-100=0 equation:

15x-0.5x^2-100=0

a = -0.5; b = 15; c = -100;
Δ = b2-4ac
Δ = 152-4·(-0.5)·(-100)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5}{2*-0.5}=\frac{-20}{-1}
=+20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5}{2*-0.5}=\frac{-10}{-1}
=+10
$