10x+25/x=-35

Solution for 10x+25/x=-35 equation:

10x+25/x=-35

We move all terms to the left:

10x+25/x-(-35)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

10x+25/x+35=0

We multiply all the terms by the denominator


10x*x+35*x+25=0

We add all the numbers together, and all the variables

35x+10x*x+25=0

Wy multiply elements

10x^2+35x+25=0

a = 10; b = 35; c = +25;
Δ = b2-4ac
Δ = 352-4·10·25
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-15}{2*10}=\frac{-50}{20}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+15}{2*10}=\frac{-20}{20}
=-1
$