11x+2/3x=37

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

11x+2/3x=37

We move all terms to the left:

11x+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


11x*3x-37*3x+2=0

Wy multiply elements

33x^2-111x+2=0

a = 33; b = -111; c = +2;
Δ = b2-4ac
Δ = -1112-4·33·2
Δ = 12057
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-111)-\sqrt{12057}}{2*33}=\frac{111-\sqrt{12057}}{66}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-111)+\sqrt{12057}}{2*33}=\frac{111+\sqrt{12057}}{66}
$