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X-5/3=4/(X-3)
We move all terms to the left:
X-5/3-(4/(X-3))=0
Domain of the equation: (X-3))!=0We calculate fractions
X∈R
X+()/3X+(-5X)/3X=0
We multiply all the terms by the denominator
X*3X+(-5X)+()=0
We add all the numbers together, and all the variables
X*3X+(-5X)=0
Wy multiply elements
3X^2+(-5X)=0
We get rid of parentheses
3X^2-5X=0
a = 3; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·3·0
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$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*3}=\frac{0}{6} =0 $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*3}=\frac{10}{6} =1+2/3 $
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