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x+x*1.05^1+x*1.05^2+x*1.05^3+x*1.05^4+x*1.05^5=68.02
We move all terms to the left:
x+x*1.05^1+x*1.05^2+x*1.05^3+x*1.05^4+x*1.05^5-(68.02)=0
We add all the numbers together, and all the variables
x+x*1.05^1+x*1.05^2+x*1.05^3+x*1.05^4+x*1.05^5-68.02=0
Wy multiply elements
x^2+x^2+x^2+x^2+x^2+x-68.02=0
We add all the numbers together, and all the variables
5x^2+x-68.02=0
a = 5; b = 1; c = -68.02;
Δ = b2-4ac
Δ = 12-4·5·(-68.02)
Δ = 1361.4
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{-(1)-\sqrt{1361.4}}{2*5}=\frac{-1-\sqrt{1361.4}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1361.4}}{2*5}=\frac{-1+\sqrt{1361.4}}{10} $
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