37/6x+2/3x=37

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

37/6x+2/3x=37

We move all terms to the left:

37/6x+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


111x/18x^2+12x/18x^2-37=0

We multiply all the terms by the denominator


111x+12x-37*18x^2=0

We add all the numbers together, and all the variables

123x-37*18x^2=0

Wy multiply elements

-666x^2+123x=0

a = -666; b = 123; c = 0;
Δ = b2-4ac
Δ = 1232-4·(-666)·0
Δ = 15129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15129}=123$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(123)-123}{2*-666}=\frac{-246}{-1332}
=41/222
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(123)+123}{2*-666}=\frac{0}{-1332}
=0
$