x2+22x+7=0

Solution for x2+22x+7=0 equation:

x2+22x+7=0

We add all the numbers together, and all the variables

x^2+22x+7=0

a = 1; b = 22; c = +7;
Δ = b2-4ac
Δ = 222-4·1·7
Δ = 456
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:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{114}}{2*1}=\frac{-22-2\sqrt{114}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{114}}{2*1}=\frac{-22+2\sqrt{114}}{2}
$