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7/4x-3=2/x+3
We move all terms to the left:
7/4x-3-(2/x+3)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: x+3)!=0We get rid of parentheses
x∈R
7/4x-2/x-3-3=0
We calculate fractions
7x/4x^2+(-8x)/4x^2-3-3=0
We add all the numbers together, and all the variables
7x/4x^2+(-8x)/4x^2-6=0
We multiply all the terms by the denominator
7x+(-8x)-6*4x^2=0
Wy multiply elements
-24x^2+7x+(-8x)=0
We get rid of parentheses
-24x^2+7x-8x=0
We add all the numbers together, and all the variables
-24x^2-1x=0
a = -24; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-24)·0
Δ = 1
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{1}=1$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-24}=\frac{0}{-48} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-24}=\frac{2}{-48} =-1/24 $
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