x^2+22x-16=38

Solution for x^2+22x-16=38 equation:

x^2+22x-16=38

We move all terms to the left:

x^2+22x-16-(38)=0

We add all the numbers together, and all the variables

x^2+22x-54=0

a = 1; b = 22; c = -54;
Δ = b2-4ac
Δ = 222-4·1·(-54)
Δ = 700
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:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-10\sqrt{7}}{2*1}=\frac{-22-10\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+10\sqrt{7}}{2*1}=\frac{-22+10\sqrt{7}}{2}
$