0.20(65-x)=x^2

Solution for 0.20(65-x)=x^2 equation:

0.20(65-x)=x^2

We move all terms to the left:

0.20(65-x)-(x^2)=0

determiningTheFunctionDomain
-x^2+0.20(65-x)=0

We add all the numbers together, and all the variables

-x^2+0.20(-1x+65)=0

We add all the numbers together, and all the variables

-1x^2+0.20(-1x+65)=0

We multiply parentheses

-1x^2-0.2x+13=0

a = -1; b = -0.2; c = +13;
Δ = b2-4ac
Δ = -0.22-4·(-1)·13
Δ = 52.04
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{52.04}}{2*-1}=\frac{0.2-\sqrt{52.04}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.2)+\sqrt{52.04}}{2*-1}=\frac{0.2+\sqrt{52.04}}{-2}
$