5/11x+4/6x=-189

Solution for 5/11x+4/6x=-189 equation:

5/11x+4/6x=-189

We move all terms to the left:

5/11x+4/6x-(-189)=0


Domain of the equation: 11x!=0

x!=0/11

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

5/11x+4/6x+189=0

We calculate fractions


30x/66x^2+44x/66x^2+189=0

We multiply all the terms by the denominator


30x+44x+189*66x^2=0

We add all the numbers together, and all the variables

74x+189*66x^2=0

Wy multiply elements

12474x^2+74x=0

a = 12474; b = 74; c = 0;
Δ = b2-4ac
Δ = 742-4·12474·0
Δ = 5476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5476}=74$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(74)-74}{2*12474}=\frac{-148}{24948}
=-37/6237
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(74)+74}{2*12474}=\frac{0}{24948}
=0
$