7x+12=x^2

Solution for 7x+12=x^2 equation:

7x+12=x^2

We move all terms to the left:

7x+12-(x^2)=0

determiningTheFunctionDomain
-x^2+7x+12=0

We add all the numbers together, and all the variables

-1x^2+7x+12=0

a = -1; b = 7; c = +12;
Δ = b2-4ac
Δ = 72-4·(-1)·12
Δ = 97
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{-(7)-\sqrt{97}}{2*-1}=\frac{-7-\sqrt{97}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{97}}{2*-1}=\frac{-7+\sqrt{97}}{-2}
$