2/5x=x+11

Solution for 2/5x=x+11 equation:

2/5x=x+11

We move all terms to the left:

2/5x-(x+11)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

2/5x-x-11=0

We multiply all the terms by the denominator


-x*5x-11*5x+2=0

Wy multiply elements

-5x^2-55x+2=0

a = -5; b = -55; c = +2;
Δ = b2-4ac
Δ = -552-4·(-5)·2
Δ = 3065
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{3065}}{2*-5}=\frac{55-\sqrt{3065}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+\sqrt{3065}}{2*-5}=\frac{55+\sqrt{3065}}{-10}
$