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x^2+15x=-31
We move all terms to the left:
x^2+15x-(-31)=0
We add all the numbers together, and all the variables
x^2+15x+31=0
a = 1; b = 15; c = +31;
Δ = b2-4ac
Δ = 152-4·1·31
Δ = 101
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{-(15)-\sqrt{101}}{2*1}=\frac{-15-\sqrt{101}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{101}}{2*1}=\frac{-15+\sqrt{101}}{2} $
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