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1/3n+12=2n-3
We move all terms to the left:
1/3n+12-(2n-3)=0
Domain of the equation: 3n!=0We get rid of parentheses
n!=0/3
n!=0
n∈R
1/3n-2n+3+12=0
We multiply all the terms by the denominator
-2n*3n+3*3n+12*3n+1=0
Wy multiply elements
-6n^2+9n+36n+1=0
We add all the numbers together, and all the variables
-6n^2+45n+1=0
a = -6; b = 45; c = +1;
Δ = b2-4ac
Δ = 452-4·(-6)·1
Δ = 2049
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-\sqrt{2049}}{2*-6}=\frac{-45-\sqrt{2049}}{-12} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2049}}{2*-6}=\frac{-45+\sqrt{2049}}{-12} $
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