5.5x+2/3x=37

Solution for 5.5x+2/3x=37 equation:

5.5x+2/3x=37

We move all terms to the left:

5.5x+2/3x-(37)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


(5.5x)*3x-37*3x+2=0

We add all the numbers together, and all the variables

(+5.5x)*3x-37*3x+2=0

We multiply parentheses

15x^2-37*3x+2=0

Wy multiply elements

15x^2-111x+2=0

a = 15; b = -111; c = +2;
Δ = b2-4ac
Δ = -1112-4·15·2
Δ = 12201
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:

$\sqrt{\Delta}=\sqrt{12201}=\sqrt{49*249}=\sqrt{49}*\sqrt{249}=7\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-111)-7\sqrt{249}}{2*15}=\frac{111-7\sqrt{249}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-111)+7\sqrt{249}}{2*15}=\frac{111+7\sqrt{249}}{30}
$