3x-2/(x+5)=16

Solution for 3x-2/(x+5)=16 equation:

3x-2/(x+5)=16

We move all terms to the left:

3x-2/(x+5)-(16)=0


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

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

x!=-5

x∈R


We multiply all the terms by the denominator


3x*(x+5)-16*(x+5)-2=0

We multiply parentheses

3x^2+15x-16x-80-2=0

We add all the numbers together, and all the variables

3x^2-1x-82=0

a = 3; b = -1; c = -82;
Δ = b2-4ac
Δ = -12-4·3·(-82)
Δ = 985
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{-(-1)-\sqrt{985}}{2*3}=\frac{1-\sqrt{985}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{985}}{2*3}=\frac{1+\sqrt{985}}{6}
$