6.66(5-x)=x^2

Solution for 6.66(5-x)=x^2 equation:

6.66(5-x)=x^2

We move all terms to the left:

6.66(5-x)-(x^2)=0

determiningTheFunctionDomain
-x^2+6.66(5-x)=0

We add all the numbers together, and all the variables

-x^2+6.66(-1x+5)=0

We add all the numbers together, and all the variables

-1x^2+6.66(-1x+5)=0

We multiply parentheses

-1x^2-6.66x+33.3=0

a = -1; b = -6.66; c = +33.3;
Δ = b2-4ac
Δ = -6.662-4·(-1)·33.3
Δ = 177.5556
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{-(-6.66)-\sqrt{177.5556}}{2*-1}=\frac{6.66-\sqrt{177.5556}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6.66)+\sqrt{177.5556}}{2*-1}=\frac{6.66+\sqrt{177.5556}}{-2}
$