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80-1/3x=1/2x+75
We move all terms to the left:
80-1/3x-(1/2x+75)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 2x+75)!=0We get rid of parentheses
x∈R
-1/3x-1/2x-75+80=0
We calculate fractions
(-2x)/6x^2+(-3x)/6x^2-75+80=0
We add all the numbers together, and all the variables
(-2x)/6x^2+(-3x)/6x^2+5=0
We multiply all the terms by the denominator
(-2x)+(-3x)+5*6x^2=0
Wy multiply elements
30x^2+(-2x)+(-3x)=0
We get rid of parentheses
30x^2-2x-3x=0
We add all the numbers together, and all the variables
30x^2-5x=0
a = 30; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·30·0
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*30}=\frac{0}{60} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*30}=\frac{10}{60} =1/6 $
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