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61/3x-57=1-1/2x
We move all terms to the left:
61/3x-57-(1-1/2x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 2x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
61/3x-(-1/2x+1)-57=0
We get rid of parentheses
61/3x+1/2x-1-57=0
We calculate fractions
122x/6x^2+3x/6x^2-1-57=0
We add all the numbers together, and all the variables
122x/6x^2+3x/6x^2-58=0
We multiply all the terms by the denominator
122x+3x-58*6x^2=0
We add all the numbers together, and all the variables
125x-58*6x^2=0
Wy multiply elements
-348x^2+125x=0
a = -348; b = 125; c = 0;
Δ = b2-4ac
Δ = 1252-4·(-348)·0
Δ = 15625
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{15625}=125$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(125)-125}{2*-348}=\frac{-250}{-696} =125/348 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(125)+125}{2*-348}=\frac{0}{-696} =0 $
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