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x/5x+2=3x+44
We move all terms to the left:
x/5x+2-(3x+44)=0
Domain of the equation: 5x!=0We get rid of parentheses
x!=0/5
x!=0
x∈R
x/5x-3x-44+2=0
We multiply all the terms by the denominator
x-3x*5x-44*5x+2*5x=0
Wy multiply elements
-15x^2+x-220x+10x=0
We add all the numbers together, and all the variables
-15x^2-209x=0
a = -15; b = -209; c = 0;
Δ = b2-4ac
Δ = -2092-4·(-15)·0
Δ = 43681
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{43681}=209$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-209)-209}{2*-15}=\frac{0}{-30} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-209)+209}{2*-15}=\frac{418}{-30} =-13+14/15 $
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