5x+140/x=-55

Solution for 5x+140/x=-55 equation:

5x+140/x=-55

We move all terms to the left:

5x+140/x-(-55)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

5x+140/x+55=0

We multiply all the terms by the denominator


5x*x+55*x+140=0

We add all the numbers together, and all the variables

55x+5x*x+140=0

Wy multiply elements

5x^2+55x+140=0

a = 5; b = 55; c = +140;
Δ = b2-4ac
Δ = 552-4·5·140
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{-(55)-15}{2*5}=\frac{-70}{10}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+15}{2*5}=\frac{-40}{10}
=-4
$