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3/5x-1/3x=4
We move all terms to the left:
3/5x-1/3x-(4)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 3x!=0We calculate fractions
x!=0/3
x!=0
x∈R
9x/15x^2+(-5x)/15x^2-4=0
We multiply all the terms by the denominator
9x+(-5x)-4*15x^2=0
Wy multiply elements
-60x^2+9x+(-5x)=0
We get rid of parentheses
-60x^2+9x-5x=0
We add all the numbers together, and all the variables
-60x^2+4x=0
a = -60; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-60)·0
Δ = 16
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{16}=4$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-60}=\frac{-8}{-120} =1/15 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-60}=\frac{0}{-120} =0 $
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