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2/3x-8=1/4x
We move all terms to the left:
2/3x-8-(1/4x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 4x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
2/3x-(+1/4x)-8=0
We get rid of parentheses
2/3x-1/4x-8=0
We calculate fractions
8x/12x^2+(-3x)/12x^2-8=0
We multiply all the terms by the denominator
8x+(-3x)-8*12x^2=0
Wy multiply elements
-96x^2+8x+(-3x)=0
We get rid of parentheses
-96x^2+8x-3x=0
We add all the numbers together, and all the variables
-96x^2+5x=0
a = -96; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-96)·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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-96}=\frac{-10}{-192} =5/96 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-96}=\frac{0}{-192} =0 $
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