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5/3x+15=5/4x-3
We move all terms to the left:
5/3x+15-(5/4x-3)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 4x-3)!=0We get rid of parentheses
x∈R
5/3x-5/4x+3+15=0
We calculate fractions
20x/12x^2+(-15x)/12x^2+3+15=0
We add all the numbers together, and all the variables
20x/12x^2+(-15x)/12x^2+18=0
We multiply all the terms by the denominator
20x+(-15x)+18*12x^2=0
Wy multiply elements
216x^2+20x+(-15x)=0
We get rid of parentheses
216x^2+20x-15x=0
We add all the numbers together, and all the variables
216x^2+5x=0
a = 216; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·216·0
Δ = 25
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{25}=5$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*216}=\frac{-10}{432} =-5/216 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*216}=\frac{0}{432} =0 $
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