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a^2+5a+1=14
We move all terms to the left:
a^2+5a+1-(14)=0
We add all the numbers together, and all the variables
a^2+5a-13=0
a = 1; b = 5; c = -13;
Δ = b2-4ac
Δ = 52-4·1·(-13)
Δ = 77
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{77}}{2*1}=\frac{-5-\sqrt{77}}{2} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{77}}{2*1}=\frac{-5+\sqrt{77}}{2} $
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