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1/3x+6=3/5x-4
We move all terms to the left:
1/3x+6-(3/5x-4)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 5x-4)!=0We get rid of parentheses
x∈R
1/3x-3/5x+4+6=0
We calculate fractions
5x/15x^2+(-9x)/15x^2+4+6=0
We add all the numbers together, and all the variables
5x/15x^2+(-9x)/15x^2+10=0
We multiply all the terms by the denominator
5x+(-9x)+10*15x^2=0
Wy multiply elements
150x^2+5x+(-9x)=0
We get rid of parentheses
150x^2+5x-9x=0
We add all the numbers together, and all the variables
150x^2-4x=0
a = 150; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·150·0
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*150}=\frac{0}{300} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*150}=\frac{8}{300} =2/75 $
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