2x+12/x=-10

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Solution for 2x+12/x=-10 equation:



2x+12/x=-10
We move all terms to the left:
2x+12/x-(-10)=0
Domain of the equation: x!=0
x∈R
We add all the numbers together, and all the variables
2x+12/x+10=0
We multiply all the terms by the denominator
2x*x+10*x+12=0
We add all the numbers together, and all the variables
10x+2x*x+12=0
Wy multiply elements
2x^2+10x+12=0
a = 2; b = 10; c = +12;
Δ = b2-4ac
Δ = 102-4·2·12
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2}{2*2}=\frac{-12}{4} =-3 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2}{2*2}=\frac{-8}{4} =-2 $

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