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x-1/3x=4.8
We move all terms to the left:
x-1/3x-(4.8)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
x-1/3x-4.8=0
We multiply all the terms by the denominator
x*3x-(4.8)*3x-1=0
We multiply parentheses
x*3x-14.4x-1=0
Wy multiply elements
3x^2-14.4x-1=0
a = 3; b = -14.4; c = -1;
Δ = b2-4ac
Δ = -14.42-4·3·(-1)
Δ = 219.36
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14.4)-\sqrt{219.36}}{2*3}=\frac{14.4-\sqrt{219.36}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14.4)+\sqrt{219.36}}{2*3}=\frac{14.4+\sqrt{219.36}}{6} $
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