3/5x+x=11

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

3/5x+x=11

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

x+3/5x-11=0

We multiply all the terms by the denominator


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

Wy multiply elements

5x^2-55x+3=0

a = 5; b = -55; c = +3;
Δ = b2-4ac
Δ = -552-4·5·3
Δ = 2965
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{2965}}{2*5}=\frac{55-\sqrt{2965}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+\sqrt{2965}}{2*5}=\frac{55+\sqrt{2965}}{10}
$