6x+261=x^2

Solution for 6x+261=x^2 equation:

6x+261=x^2

We move all terms to the left:

6x+261-(x^2)=0

determiningTheFunctionDomain
-x^2+6x+261=0

We add all the numbers together, and all the variables

-1x^2+6x+261=0

a = -1; b = 6; c = +261;
Δ = b2-4ac
Δ = 62-4·(-1)·261
Δ = 1080
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:

$\sqrt{\Delta}=\sqrt{1080}=\sqrt{36*30}=\sqrt{36}*\sqrt{30}=6\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{30}}{2*-1}=\frac{-6-6\sqrt{30}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{30}}{2*-1}=\frac{-6+6\sqrt{30}}{-2}
$