x^2-7=-x+7

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

x^2-7=-x+7

We move all terms to the left:

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

We add all the numbers together, and all the variables

x^2-(-1x+7)-7=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2+x-14=0

a = 1; b = 1; c = -14;
Δ = b2-4ac
Δ = 12-4·1·(-14)
Δ = 57
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{-(1)-\sqrt{57}}{2*1}=\frac{-1-\sqrt{57}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{57}}{2*1}=\frac{-1+\sqrt{57}}{2}
$