x^2=5x-0.5x^2

Solution for x^2=5x-0.5x^2 equation:

x^2=5x-0.5x^2

We move all terms to the left:

x^2-(5x-0.5x^2)=0

We get rid of parentheses

x^2+0.5x^2-5x=0

We add all the numbers together, and all the variables

1.5x^2-5x=0

a = 1.5; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·1.5·0
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{-(-5)-5}{2*1.5}=\frac{0}{3}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*1.5}=\frac{10}{3}
=3+1/3
$