x2+13x+22=7

Solution for x2+13x+22=7 equation:

x2+13x+22=7

We move all terms to the left:

x2+13x+22-(7)=0

We add all the numbers together, and all the variables

x^2+13x+15=0

a = 1; b = 13; c = +15;
Δ = b2-4ac
Δ = 132-4·1·15
Δ = 109
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{109}}{2*1}=\frac{-13-\sqrt{109}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{109}}{2*1}=\frac{-13+\sqrt{109}}{2}
$