5x+2+x^2-9+x^2-7x+12=63

Solution for 5x+2+x^2-9+x^2-7x+12=63 equation:

5x+2+x^2-9+x^2-7x+12=63

We move all terms to the left:

5x+2+x^2-9+x^2-7x+12-(63)=0

We add all the numbers together, and all the variables

2x^2-2x-58=0

a = 2; b = -2; c = -58;
Δ = b2-4ac
Δ = -22-4·2·(-58)
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6\sqrt{13}}{2*2}=\frac{2-6\sqrt{13}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6\sqrt{13}}{2*2}=\frac{2+6\sqrt{13}}{4}
$