8x=x^2-10

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

8x=x^2-10

We move all terms to the left:

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

We get rid of parentheses

-x^2+8x+10=0

We add all the numbers together, and all the variables

-1x^2+8x+10=0

a = -1; b = 8; c = +10;
Δ = b2-4ac
Δ = 82-4·(-1)·10
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{26}}{2*-1}=\frac{-8-2\sqrt{26}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{26}}{2*-1}=\frac{-8+2\sqrt{26}}{-2}
$