x+(1/3x+5)=48

Solution for x+(1/3x+5)=48 equation:

x+(1/3x+5)=48

We move all terms to the left:

x+(1/3x+5)-(48)=0


Domain of the equation: 3x+5)!=0

x∈R


We get rid of parentheses

x+1/3x+5-48=0

We multiply all the terms by the denominator


x*3x+5*3x-48*3x+1=0

Wy multiply elements

3x^2+15x-144x+1=0

We add all the numbers together, and all the variables

3x^2-129x+1=0

a = 3; b = -129; c = +1;
Δ = b2-4ac
Δ = -1292-4·3·1
Δ = 16629
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{-(-129)-\sqrt{16629}}{2*3}=\frac{129-\sqrt{16629}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-129)+\sqrt{16629}}{2*3}=\frac{129+\sqrt{16629}}{6}
$