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2n+3=1/2n+12
We move all terms to the left:
2n+3-(1/2n+12)=0
Domain of the equation: 2n+12)!=0We get rid of parentheses
n∈R
2n-1/2n-12+3=0
We multiply all the terms by the denominator
2n*2n-12*2n+3*2n-1=0
Wy multiply elements
4n^2-24n+6n-1=0
We add all the numbers together, and all the variables
4n^2-18n-1=0
a = 4; b = -18; c = -1;
Δ = b2-4ac
Δ = -182-4·4·(-1)
Δ = 340
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{85}}{2*4}=\frac{18-2\sqrt{85}}{8} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{85}}{2*4}=\frac{18+2\sqrt{85}}{8} $
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