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1/3x-2/5x=7/15
We move all terms to the left:
1/3x-2/5x-(7/15)=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
1/3x-2/5x-(+7/15)=0
We get rid of parentheses
1/3x-2/5x-7/15=0
We calculate fractions
(-525x^2)/225x^2+75x/225x^2+(-90x)/225x^2=0
We multiply all the terms by the denominator
(-525x^2)+75x+(-90x)=0
We get rid of parentheses
-525x^2+75x-90x=0
We add all the numbers together, and all the variables
-525x^2-15x=0
a = -525; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·(-525)·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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*-525}=\frac{0}{-1050} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*-525}=\frac{30}{-1050} =-1/35 $
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