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X=3X/4X+5
We move all terms to the left:
X-(3X/4X+5)=0
Domain of the equation: 4X+5)!=0We get rid of parentheses
X∈R
X-3X/4X-5=0
We multiply all the terms by the denominator
X*4X-3X-5*4X=0
We add all the numbers together, and all the variables
-3X+X*4X-5*4X=0
Wy multiply elements
4X^2-3X-20X=0
We add all the numbers together, and all the variables
4X^2-23X=0
a = 4; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·4·0
Δ = 529
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{529}=23$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*4}=\frac{0}{8} =0 $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*4}=\frac{46}{8} =5+3/4 $
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