x+5=5/3x-2

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

x+5=5/3x-2

We move all terms to the left:

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


Domain of the equation: 3x-2)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

3x^2+6x+15x-5=0

We add all the numbers together, and all the variables

3x^2+21x-5=0

a = 3; b = 21; c = -5;
Δ = b2-4ac
Δ = 212-4·3·(-5)
Δ = 501
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{-(21)-\sqrt{501}}{2*3}=\frac{-21-\sqrt{501}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{501}}{2*3}=\frac{-21+\sqrt{501}}{6}
$