X2+10x+22=31

Solution for X2+10x+22=31 equation:

X2+10X+22=31

We move all terms to the left:

X2+10X+22-(31)=0

We add all the numbers together, and all the variables

X^2+10X-9=0

a = 1; b = 10; c = -9;
Δ = b2-4ac
Δ = 102-4·1·(-9)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{34}}{2*1}=\frac{-10-2\sqrt{34}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{34}}{2*1}=\frac{-10+2\sqrt{34}}{2}
$