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1/2x+2+1/3x=10
We move all terms to the left:
1/2x+2+1/3x-(10)=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!=0/3
x!=0
x∈R
1/2x+1/3x-8=0
We calculate fractions
3x/6x^2+2x/6x^2-8=0
We multiply all the terms by the denominator
3x+2x-8*6x^2=0
We add all the numbers together, and all the variables
5x-8*6x^2=0
Wy multiply elements
-48x^2+5x=0
a = -48; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-48)·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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-48}=\frac{-10}{-96} =5/48 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-48}=\frac{0}{-96} =0 $
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