.083-8.3x=x^2

Solution for .083-8.3x=x^2 equation:

.083-8.3x=x^2

We move all terms to the left:

.083-8.3x-(x^2)=0

determiningTheFunctionDomain
-x^2-8.3x+.083=0

We add all the numbers together, and all the variables

-1x^2-8.3x+0.083=0

a = -1; b = -8.3; c = +0.083;
Δ = b2-4ac
Δ = -8.32-4·(-1)·0.083
Δ = 69.222
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{-(-8.3)-\sqrt{69.222}}{2*-1}=\frac{8.3-\sqrt{69.222}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8.3)+\sqrt{69.222}}{2*-1}=\frac{8.3+\sqrt{69.222}}{-2}
$