3x+1+2/3x+6=90

Solution for 3x+1+2/3x+6=90 equation:

3x+1+2/3x+6=90

We move all terms to the left:

3x+1+2/3x+6-(90)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

3x+2/3x-83=0

We multiply all the terms by the denominator


3x*3x-83*3x+2=0

Wy multiply elements

9x^2-249x+2=0

a = 9; b = -249; c = +2;
Δ = b2-4ac
Δ = -2492-4·9·2
Δ = 61929
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:

$\sqrt{\Delta}=\sqrt{61929}=\sqrt{9*6881}=\sqrt{9}*\sqrt{6881}=3\sqrt{6881}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-249)-3\sqrt{6881}}{2*9}=\frac{249-3\sqrt{6881}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-249)+3\sqrt{6881}}{2*9}=\frac{249+3\sqrt{6881}}{18}
$