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4x+7/3x=31
We move all terms to the left:
4x+7/3x-(31)=0
Domain of the equation: 3x!=0We multiply all the terms by the denominator
x!=0/3
x!=0
x∈R
4x*3x-31*3x+7=0
Wy multiply elements
12x^2-93x+7=0
a = 12; b = -93; c = +7;
Δ = b2-4ac
Δ = -932-4·12·7
Δ = 8313
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{-(-93)-\sqrt{8313}}{2*12}=\frac{93-\sqrt{8313}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-93)+\sqrt{8313}}{2*12}=\frac{93+\sqrt{8313}}{24} $
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