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6/4x-4=2/3x-2
We move all terms to the left:
6/4x-4-(2/3x-2)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 3x-2)!=0We get rid of parentheses
x∈R
6/4x-2/3x+2-4=0
We calculate fractions
18x/12x^2+(-8x)/12x^2+2-4=0
We add all the numbers together, and all the variables
18x/12x^2+(-8x)/12x^2-2=0
We multiply all the terms by the denominator
18x+(-8x)-2*12x^2=0
Wy multiply elements
-24x^2+18x+(-8x)=0
We get rid of parentheses
-24x^2+18x-8x=0
We add all the numbers together, and all the variables
-24x^2+10x=0
a = -24; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-24)·0
Δ = 100
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{100}=10$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-24}=\frac{-20}{-48} =5/12 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-24}=\frac{0}{-48} =0 $
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