25/3x=2x+1

Solution for 25/3x=2x+1 equation:

25/3x=2x+1

We move all terms to the left:

25/3x-(2x+1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

25/3x-2x-1=0

We multiply all the terms by the denominator


-2x*3x-1*3x+25=0

Wy multiply elements

-6x^2-3x+25=0

a = -6; b = -3; c = +25;
Δ = b2-4ac
Δ = -32-4·(-6)·25
Δ = 609
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{-(-3)-\sqrt{609}}{2*-6}=\frac{3-\sqrt{609}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{609}}{2*-6}=\frac{3+\sqrt{609}}{-12}
$