x+5=5/3x+12

Solution for x+5=5/3x+12 equation:

x+5=5/3x+12

We move all terms to the left:

x+5-(5/3x+12)=0


Domain of the equation: 3x+12)!=0

x∈R


We get rid of parentheses

x-5/3x-12+5=0

We multiply all the terms by the denominator


x*3x-12*3x+5*3x-5=0

Wy multiply elements

3x^2-36x+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}
$