5x=2/3x-13

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Solution for 5x=2/3x-13 equation:



5x=2/3x-13
We move all terms to the left:
5x-(2/3x-13)=0
Domain of the equation: 3x-13)!=0
x∈R
We get rid of parentheses
5x-2/3x+13=0
We multiply all the terms by the denominator
5x*3x+13*3x-2=0
Wy multiply elements
15x^2+39x-2=0
a = 15; b = 39; c = -2;
Δ = b2-4ac
Δ = 392-4·15·(-2)
Δ = 1641
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{-(39)-\sqrt{1641}}{2*15}=\frac{-39-\sqrt{1641}}{30} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+\sqrt{1641}}{2*15}=\frac{-39+\sqrt{1641}}{30} $

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