12x+15=x^2

Solution for 12x+15=x^2 equation:

12x+15=x^2

We move all terms to the left:

12x+15-(x^2)=0

determiningTheFunctionDomain
-x^2+12x+15=0

We add all the numbers together, and all the variables

-1x^2+12x+15=0

a = -1; b = 12; c = +15;
Δ = b2-4ac
Δ = 122-4·(-1)·15
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{51}}{2*-1}=\frac{-12-2\sqrt{51}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{51}}{2*-1}=\frac{-12+2\sqrt{51}}{-2}
$