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3/4x+2-1/3x=12
We move all terms to the left:
3/4x+2-1/3x-(12)=0
Domain of the equation: 4x!=0
x!=0/4
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
3/4x-1/3x-10=0
We calculate fractions
9x/12x^2+(-4x)/12x^2-10=0
We multiply all the terms by the denominator
9x+(-4x)-10*12x^2=0
Wy multiply elements
-120x^2+9x+(-4x)=0
We get rid of parentheses
-120x^2+9x-4x=0
We add all the numbers together, and all the variables
-120x^2+5x=0
a = -120; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-120)·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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-120}=\frac{-10}{-240} =1/24 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-120}=\frac{0}{-240} =0 $
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