x+2/5x=5

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

x+2/5x=5

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

5x^2-25x+2=0

a = 5; b = -25; c = +2;
Δ = b2-4ac
Δ = -252-4·5·2
Δ = 585
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-3\sqrt{65}}{2*5}=\frac{25-3\sqrt{65}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+3\sqrt{65}}{2*5}=\frac{25+3\sqrt{65}}{10}
$