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4x+5/4-5x/x-3=x
We move all terms to the left:
4x+5/4-5x/x-3-(x)=0
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
3x-5x/x-3+5/4=0
We calculate fractions
3x+(-20x)/4x+5x/4x-3=0
We multiply all the terms by the denominator
3x*4x+(-20x)+5x-3*4x=0
We add all the numbers together, and all the variables
5x+3x*4x+(-20x)-3*4x=0
Wy multiply elements
12x^2+5x+(-20x)-12x=0
We get rid of parentheses
12x^2+5x-20x-12x=0
We add all the numbers together, and all the variables
12x^2-27x=0
a = 12; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·12·0
Δ = 729
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{729}=27$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*12}=\frac{0}{24} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*12}=\frac{54}{24} =2+1/4 $
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