X^2-10x+8=22

Solution for X^2-10x+8=22 equation:

X^2-10X+8=22

We move all terms to the left:

X^2-10X+8-(22)=0

We add all the numbers together, and all the variables

X^2-10X-14=0

a = 1; b = -10; c = -14;
Δ = b2-4ac
Δ = -102-4·1·(-14)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{39}}{2*1}=\frac{10-2\sqrt{39}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{39}}{2*1}=\frac{10+2\sqrt{39}}{2}
$