X2=22x+10

Solution for X2=22x+10 equation:

X2=22X+10

We move all terms to the left:

X2-(22X+10)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

X^2-22X-10=0

a = 1; b = -22; c = -10;
Δ = b2-4ac
Δ = -222-4·1·(-10)
Δ = 524
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:

$\sqrt{\Delta}=\sqrt{524}=\sqrt{4*131}=\sqrt{4}*\sqrt{131}=2\sqrt{131}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{131}}{2*1}=\frac{22-2\sqrt{131}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{131}}{2*1}=\frac{22+2\sqrt{131}}{2}
$