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5/6x+2=-7+1/2x
We move all terms to the left:
5/6x+2-(-7+1/2x)=0
Domain of the equation: 6x!=0
x!=0/6
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
5/6x-(1/2x-7)+2=0
We get rid of parentheses
5/6x-1/2x+7+2=0
We calculate fractions
10x/12x^2+(-6x)/12x^2+7+2=0
We add all the numbers together, and all the variables
10x/12x^2+(-6x)/12x^2+9=0
We multiply all the terms by the denominator
10x+(-6x)+9*12x^2=0
Wy multiply elements
108x^2+10x+(-6x)=0
We get rid of parentheses
108x^2+10x-6x=0
We add all the numbers together, and all the variables
108x^2+4x=0
a = 108; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·108·0
Δ = 16
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{16}=4$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*108}=\frac{-8}{216} =-1/27 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*108}=\frac{0}{216} =0 $
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