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n=3/4n-7
We move all terms to the left:
n-(3/4n-7)=0
Domain of the equation: 4n-7)!=0We get rid of parentheses
n∈R
n-3/4n+7=0
We multiply all the terms by the denominator
n*4n+7*4n-3=0
Wy multiply elements
4n^2+28n-3=0
a = 4; b = 28; c = -3;
Δ = b2-4ac
Δ = 282-4·4·(-3)
Δ = 832
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-8\sqrt{13}}{2*4}=\frac{-28-8\sqrt{13}}{8} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+8\sqrt{13}}{2*4}=\frac{-28+8\sqrt{13}}{8} $
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