x=15x-0.5x^2

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

x=15x-0.5x^2

We move all terms to the left:

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

We get rid of parentheses

0.5x^2-15x+x=0

We add all the numbers together, and all the variables

0.5x^2-14x=0

a = 0.5; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·0.5·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*0.5}=\frac{0}{1}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*0.5}=\frac{28}{1}
=28
$