8x-10=10-x^2

Solution for 8x-10=10-x^2 equation:

8x-10=10-x^2

We move all terms to the left:

8x-10-(10-x^2)=0

We get rid of parentheses

x^2+8x-10-10=0

We add all the numbers together, and all the variables

x^2+8x-20=0

a = 1; b = 8; c = -20;
Δ = b2-4ac
Δ = 82-4·1·(-20)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-12}{2*1}=\frac{-20}{2}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12}{2*1}=\frac{4}{2}
=2
$