7/x+5+5/5x+25=-10

Solution for 7/x+5+5/5x+25=-10 equation:

7/x+5+5/5x+25=-10

We move all terms to the left:

7/x+5+5/5x+25-(-10)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

7/x+5/5x+40=0

We calculate fractions


35x/5x^2+5x/5x^2+40=0

We multiply all the terms by the denominator


35x+5x+40*5x^2=0

We add all the numbers together, and all the variables

40x+40*5x^2=0

Wy multiply elements

200x^2+40x=0

a = 200; b = 40; c = 0;
Δ = b2-4ac
Δ = 402-4·200·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40}{2*200}=\frac{-80}{400}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40}{2*200}=\frac{0}{400}
=0
$