x2+22x=15

Solution for x2+22x=15 equation:

x2+22x=15

We move all terms to the left:

x2+22x-(15)=0

We add all the numbers together, and all the variables

x^2+22x-15=0

a = 1; b = 22; c = -15;
Δ = b2-4ac
Δ = 222-4·1·(-15)
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-4\sqrt{34}}{2*1}=\frac{-22-4\sqrt{34}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+4\sqrt{34}}{2*1}=\frac{-22+4\sqrt{34}}{2}
$