11/6x+2/3x=37

Solution for 11/6x+2/3x=37 equation:

11/6x+2/3x=37

We move all terms to the left:

11/6x+2/3x-(37)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


33x/18x^2+12x/18x^2-37=0

We multiply all the terms by the denominator


33x+12x-37*18x^2=0

We add all the numbers together, and all the variables

45x-37*18x^2=0

Wy multiply elements

-666x^2+45x=0

a = -666; b = 45; c = 0;
Δ = b2-4ac
Δ = 452-4·(-666)·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-45}{2*-666}=\frac{-90}{-1332}
=5/74
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+45}{2*-666}=\frac{0}{-1332}
=0
$