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

Solution for (3-x)/(2x+5)=x/3 equation:

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

We move all terms to the left:

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


Domain of the equation: (2x+5)!=0

We move all terms containing x to the left, all other terms to the right

2x!=-5

x!=-5/2

x!=-2+1/2

x∈R


We add all the numbers together, and all the variables

(-1x+3)/(2x+5)-(+x/3)=0

We get rid of parentheses

(-1x+3)/(2x+5)-x/3=0

We calculate fractions


(-2x^2-5x)/(6x+15)+(-3x+9)/(6x+15)=0

We multiply all the terms by the denominator


(-2x^2-5x)+(-3x+9)=0

We get rid of parentheses

-2x^2-5x-3x+9=0

We add all the numbers together, and all the variables

-2x^2-8x+9=0

a = -2; b = -8; c = +9;
Δ = b2-4ac
Δ = -82-4·(-2)·9
Δ = 136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{34}}{2*-2}=\frac{8-2\sqrt{34}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{34}}{2*-2}=\frac{8+2\sqrt{34}}{-4}
$