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8/x=9/3x-7
We move all terms to the left:
8/x-(9/3x-7)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 3x-7)!=0We get rid of parentheses
x∈R
8/x-9/3x+7=0
We calculate fractions
24x/3x^2+(-9x)/3x^2+7=0
We multiply all the terms by the denominator
24x+(-9x)+7*3x^2=0
Wy multiply elements
21x^2+24x+(-9x)=0
We get rid of parentheses
21x^2+24x-9x=0
We add all the numbers together, and all the variables
21x^2+15x=0
a = 21; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·21·0
Δ = 225
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{225}=15$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*21}=\frac{-30}{42} =-5/7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*21}=\frac{0}{42} =0 $
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