(0.2-x)*1.8=x^2

Solution for (0.2-x)*1.8=x^2 equation:

(0.2-x)*1.8=x^2

We move all terms to the left:

(0.2-x)*1.8-(x^2)=0

determiningTheFunctionDomain
-x^2+(0.2-x)*1.8=0

We add all the numbers together, and all the variables

-x^2+(-1x+0.2)*1.8=0

We add all the numbers together, and all the variables

-1x^2+(-1x+0.2)*1.8=0

We multiply parentheses

-1x^2-1.8x+0.36=0

a = -1; b = -1.8; c = +0.36;
Δ = b2-4ac
Δ = -1.82-4·(-1)·0.36
Δ = 4.68
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{-(-1.8)-\sqrt{4.68}}{2*-1}=\frac{1.8-\sqrt{4.68}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.8)+\sqrt{4.68}}{2*-1}=\frac{1.8+\sqrt{4.68}}{-2}
$