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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} $
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