5x+30/x=-25

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Solution for 5x+30/x=-25 equation:



5x+30/x=-25
We move all terms to the left:
5x+30/x-(-25)=0
Domain of the equation: x!=0
x∈R
We add all the numbers together, and all the variables
5x+30/x+25=0
We multiply all the terms by the denominator
5x*x+25*x+30=0
We add all the numbers together, and all the variables
25x+5x*x+30=0
Wy multiply elements
5x^2+25x+30=0
a = 5; b = 25; c = +30;
Δ = b2-4ac
Δ = 252-4·5·30
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-5}{2*5}=\frac{-30}{10} =-3 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+5}{2*5}=\frac{-20}{10} =-2 $

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