2/3x=5x+3

Solution for 2/3x=5x+3 equation:

2/3x=5x+3

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-5x-3=0

We multiply all the terms by the denominator


-5x*3x-3*3x+2=0

Wy multiply elements

-15x^2-9x+2=0

a = -15; b = -9; c = +2;
Δ = b2-4ac
Δ = -92-4·(-15)·2
Δ = 201
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{-(-9)-\sqrt{201}}{2*-15}=\frac{9-\sqrt{201}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{201}}{2*-15}=\frac{9+\sqrt{201}}{-30}
$