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5*3^2x+2=135*3^x+1
We move all terms to the left:
5*3^2x+2-(135*3^x+1)=0
Wy multiply elements
15x^2-(135*3^x+1)+2=0
We get rid of parentheses
15x^2-135*3^x-1+2=0
We add all the numbers together, and all the variables
15x^2-135*3^x+1=0
Wy multiply elements
15x^2-405x+1=0
a = 15; b = -405; c = +1;
Δ = b2-4ac
Δ = -4052-4·15·1
Δ = 163965
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{-(-405)-\sqrt{163965}}{2*15}=\frac{405-\sqrt{163965}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-405)+\sqrt{163965}}{2*15}=\frac{405+\sqrt{163965}}{30} $
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