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3/4x+6x=81
We move all terms to the left:
3/4x+6x-(81)=0
Domain of the equation: 4x!=0We add all the numbers together, and all the variables
x!=0/4
x!=0
x∈R
6x+3/4x-81=0
We multiply all the terms by the denominator
6x*4x-81*4x+3=0
Wy multiply elements
24x^2-324x+3=0
a = 24; b = -324; c = +3;
Δ = b2-4ac
Δ = -3242-4·24·3
Δ = 104688
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{104688}=\sqrt{144*727}=\sqrt{144}*\sqrt{727}=12\sqrt{727}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-324)-12\sqrt{727}}{2*24}=\frac{324-12\sqrt{727}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-324)+12\sqrt{727}}{2*24}=\frac{324+12\sqrt{727}}{48} $
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