5x+66=x^2

Solution for 5x+66=x^2 equation:

5x+66=x^2

We move all terms to the left:

5x+66-(x^2)=0

determiningTheFunctionDomain
-x^2+5x+66=0

We add all the numbers together, and all the variables

-1x^2+5x+66=0

a = -1; b = 5; c = +66;
Δ = b2-4ac
Δ = 52-4·(-1)·66
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-17}{2*-1}=\frac{-22}{-2}
=+11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+17}{2*-1}=\frac{12}{-2}
=-6
$