-2x=-1/3x-11

Solution for -2x=-1/3x-11 equation:

-2x=-1/3x-11

We move all terms to the left:

-2x-(-1/3x-11)=0


Domain of the equation: 3x-11)!=0

x∈R


We get rid of parentheses

-2x+1/3x+11=0

We multiply all the terms by the denominator


-2x*3x+11*3x+1=0

Wy multiply elements

-6x^2+33x+1=0

a = -6; b = 33; c = +1;
Δ = b2-4ac
Δ = 332-4·(-6)·1
Δ = 1113
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{-(33)-\sqrt{1113}}{2*-6}=\frac{-33-\sqrt{1113}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{1113}}{2*-6}=\frac{-33+\sqrt{1113}}{-12}
$