/11x-3=5x+11

Solution for /11x-3=5x+11 equation:

/11x-3=5x+11

We move all terms to the left:

/11x-3-(5x+11)=0


Domain of the equation: 11x!=0

x!=0/11

x!=0

x∈R


We get rid of parentheses

/11x-5x-11-3=0

We multiply all the terms by the denominator


-5x*11x-11*11x-3*11x+=0

We add all the numbers together, and all the variables

-5x*11x-11*11x-3*11x=0

Wy multiply elements

-55x^2-121x-33x=0

We add all the numbers together, and all the variables

-55x^2-154x=0

a = -55; b = -154; c = 0;
Δ = b2-4ac
Δ = -1542-4·(-55)·0
Δ = 23716
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{23716}=154$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-154)-154}{2*-55}=\frac{0}{-110}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-154)+154}{2*-55}=\frac{308}{-110}
=-2+4/5
$