2/3x=5x-13

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



2/3x=5x-13

We move all terms to the left:

2/3x-(5x-13)=0



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



We get rid of parentheses

2/3x-5x+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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