2x+5=x^2-7

Solution for 2x+5=x^2-7 equation:

2x+5=x^2-7

We move all terms to the left:

2x+5-(x^2-7)=0

We get rid of parentheses

-x^2+2x+7+5=0

We add all the numbers together, and all the variables

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

a = -1; b = 2; c = +12;
Δ = b2-4ac
Δ = 22-4·(-1)·12
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{13}}{2*-1}=\frac{-2-2\sqrt{13}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{13}}{2*-1}=\frac{-2+2\sqrt{13}}{-2}
$