0.5*x^2=0.9*x

Solution for 0.5*x^2=0.9*x equation:

0.5x^2=0.9x

We move all terms to the left:

0.5x^2-(0.9x)=0

We add all the numbers together, and all the variables

0.5x^2-(+0.9x)=0

We get rid of parentheses

0.5x^2-0.9x=0

a = 0.5; b = -0.9; c = 0;
Δ = b2-4ac
Δ = -0.92-4·0.5·0
Δ = 0.81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.9)-\sqrt{0.81}}{2*0.5}=\frac{0.9-\sqrt{0.81}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.9)+\sqrt{0.81}}{2*0.5}=\frac{0.9+\sqrt{0.81}}{1}
$