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7/3x+2/5x=2/30
We move all terms to the left:
7/3x+2/5x-(2/30)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
7/3x+2/5x-(+2/30)=0
We get rid of parentheses
7/3x+2/5x-2/30=0
We calculate fractions
(-150x^2)/1350x^2+3150x/1350x^2+540x/1350x^2=0
We multiply all the terms by the denominator
(-150x^2)+3150x+540x=0
We add all the numbers together, and all the variables
(-150x^2)+3690x=0
We get rid of parentheses
-150x^2+3690x=0
a = -150; b = 3690; c = 0;
Δ = b2-4ac
Δ = 36902-4·(-150)·0
Δ = 13616100
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{13616100}=3690$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3690)-3690}{2*-150}=\frac{-7380}{-300} =24+3/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3690)+3690}{2*-150}=\frac{0}{-300} =0 $
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