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1/2x+6=11-1/3x
We move all terms to the left:
1/2x+6-(11-1/3x)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 3x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
1/2x-(-1/3x+11)+6=0
We get rid of parentheses
1/2x+1/3x-11+6=0
We calculate fractions
3x/6x^2+2x/6x^2-11+6=0
We add all the numbers together, and all the variables
3x/6x^2+2x/6x^2-5=0
We multiply all the terms by the denominator
3x+2x-5*6x^2=0
We add all the numbers together, and all the variables
5x-5*6x^2=0
Wy multiply elements
-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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-30}=\frac{-10}{-60} =1/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-30}=\frac{0}{-60} =0 $
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