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4/3x+1=2x-1
We move all terms to the left:
4/3x+1-(2x-1)=0
Domain of the equation: 3x!=0We get rid of parentheses
x!=0/3
x!=0
x∈R
4/3x-2x+1+1=0
We multiply all the terms by the denominator
-2x*3x+1*3x+1*3x+4=0
Wy multiply elements
-6x^2+3x+3x+4=0
We add all the numbers together, and all the variables
-6x^2+6x+4=0
a = -6; b = 6; c = +4;
Δ = b2-4ac
Δ = 62-4·(-6)·4
Δ = 132
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{33}}{2*-6}=\frac{-6-2\sqrt{33}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{33}}{2*-6}=\frac{-6+2\sqrt{33}}{-12} $
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