x=5+3x(-2/3)

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Solution for x=5+3x(-2/3) equation:



x=5+3x(-2/3)
We move all terms to the left:
x-(5+3x(-2/3))=0
We multiply all the terms by the denominator
x*3))-(5+3x(-2=0
Wy multiply elements
3x^2-2=0
a = 3; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·3·(-2)
Δ = 24
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:
$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6}}{2*3}=\frac{0-2\sqrt{6}}{6} =-\frac{2\sqrt{6}}{6} =-\frac{\sqrt{6}}{3} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6}}{2*3}=\frac{0+2\sqrt{6}}{6} =\frac{2\sqrt{6}}{6} =\frac{\sqrt{6}}{3} $

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