x+7=x^2+3x-9

Solution for x+7=x^2+3x-9 equation:

x+7=x^2+3x-9

We move all terms to the left:

x+7-(x^2+3x-9)=0

We get rid of parentheses

-x^2+x-3x+9+7=0

We add all the numbers together, and all the variables

-1x^2-2x+16=0

a = -1; b = -2; c = +16;
Δ = b2-4ac
Δ = -22-4·(-1)·16
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{17}}{2*-1}=\frac{2-2\sqrt{17}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{17}}{2*-1}=\frac{2+2\sqrt{17}}{-2}
$