5x=2/3x+13

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}
$