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2/3x+7/5x=2/15
We move all terms to the left:
2/3x+7/5x-(2/15)=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
2/3x+7/5x-(+2/15)=0
We get rid of parentheses
2/3x+7/5x-2/15=0
We calculate fractions
(-150x^2)/225x^2+150x/225x^2+315x/225x^2=0
We multiply all the terms by the denominator
(-150x^2)+150x+315x=0
We add all the numbers together, and all the variables
(-150x^2)+465x=0
We get rid of parentheses
-150x^2+465x=0
a = -150; b = 465; c = 0;
Δ = b2-4ac
Δ = 4652-4·(-150)·0
Δ = 216225
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{216225}=465$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(465)-465}{2*-150}=\frac{-930}{-300} =3+1/10 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(465)+465}{2*-150}=\frac{0}{-300} =0 $
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