1/3x+2+x=90

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

1/3x+2+x=90

We move all terms to the left:

1/3x+2+x-(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

x+1/3x-88=0

We multiply all the terms by the denominator


x*3x-88*3x+1=0

Wy multiply elements

3x^2-264x+1=0

a = 3; b = -264; c = +1;
Δ = b2-4ac
Δ = -2642-4·3·1
Δ = 69684
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:

$\sqrt{\Delta}=\sqrt{69684}=\sqrt{4*17421}=\sqrt{4}*\sqrt{17421}=2\sqrt{17421}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-264)-2\sqrt{17421}}{2*3}=\frac{264-2\sqrt{17421}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-264)+2\sqrt{17421}}{2*3}=\frac{264+2\sqrt{17421}}{6}
$