x-5=-x2

Solution for x-5=-x2 equation:

x-5=-x2

We move all terms to the left:

x-5-(-x2)=0

We add all the numbers together, and all the variables

-(-1x^2)+x-5=0

We get rid of parentheses

1x^2+x-5=0

We add all the numbers together, and all the variables

x^2+x-5=0

a = 1; b = 1; c = -5;
Δ = b2-4ac
Δ = 12-4·1·(-5)
Δ = 21
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{21}}{2*1}=\frac{-1-\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{21}}{2*1}=\frac{-1+\sqrt{21}}{2}
$