x+5/11x=5

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

x+5/11x=5

We move all terms to the left:

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


Domain of the equation: 11x!=0

x!=0/11

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

11x^2-55x+5=0

a = 11; b = -55; c = +5;
Δ = b2-4ac
Δ = -552-4·11·5
Δ = 2805
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{-(-55)-\sqrt{2805}}{2*11}=\frac{55-\sqrt{2805}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+\sqrt{2805}}{2*11}=\frac{55+\sqrt{2805}}{22}
$