45+6x=x^2

Solution for 45+6x=x^2 equation:

45+6x=x^2

We move all terms to the left:

45+6x-(x^2)=0

determiningTheFunctionDomain
-x^2+6x+45=0

We add all the numbers together, and all the variables

-1x^2+6x+45=0

a = -1; b = 6; c = +45;
Δ = b2-4ac
Δ = 62-4·(-1)·45
Δ = 216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{6}}{2*-1}=\frac{-6-6\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{6}}{2*-1}=\frac{-6+6\sqrt{6}}{-2}
$