5/x+5/5x=6

Solution for 5/x+5/5x=6 equation:

5/x+5/5x=6

We move all terms to the left:

5/x+5/5x-(6)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


25x/5x^2+5x/5x^2-6=0

We multiply all the terms by the denominator


25x+5x-6*5x^2=0

We add all the numbers together, and all the variables

30x-6*5x^2=0

Wy multiply elements

-30x^2+30x=0

a = -30; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·(-30)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*-30}=\frac{-60}{-60}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*-30}=\frac{0}{-60}
=0
$