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5x+3x/2x+4x=40
We move all terms to the left:
5x+3x/2x+4x-(40)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
9x+3x/2x-40=0
We multiply all the terms by the denominator
9x*2x+3x-40*2x=0
We add all the numbers together, and all the variables
3x+9x*2x-40*2x=0
Wy multiply elements
18x^2+3x-80x=0
We add all the numbers together, and all the variables
18x^2-77x=0
a = 18; b = -77; c = 0;
Δ = b2-4ac
Δ = -772-4·18·0
Δ = 5929
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{5929}=77$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-77)-77}{2*18}=\frac{0}{36} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-77)+77}{2*18}=\frac{154}{36} =4+5/18 $
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