x^2=0.2*x+0.15

Solution for x^2=0.2*x+0.15 equation:

x^2=0.2x+0.15

We move all terms to the left:

x^2-(0.2x+0.15)=0

We get rid of parentheses

x^2-0.2x-0.15=0

a = 1; b = -0.2; c = -0.15;
Δ = b2-4ac
Δ = -0.22-4·1·(-0.15)
Δ = 0.64
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{-(-0.2)-\sqrt{0.64}}{2*1}=\frac{0.2-\sqrt{0.64}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.2)+\sqrt{0.64}}{2*1}=\frac{0.2+\sqrt{0.64}}{2}
$