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a*a=a+1

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Solution for a*a=a+1 equation:



a*a=a+1
We move all terms to the left:
a*a-(a+1)=0
Wy multiply elements
a^2-(a+1)=0
We get rid of parentheses
a^2-a-1=0
We add all the numbers together, and all the variables
a^2-1a-1=0
a = 1; b = -1; c = -1;
Δ = b2-4ac
Δ = -12-4·1·(-1)
Δ = 5
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{-(-1)-\sqrt{5}}{2*1}=\frac{1-\sqrt{5}}{2}
a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{5}}{2*1}=\frac{1+\sqrt{5}}{2}

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