7/x-2+5/5x-10=11

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Solution for 7/x-2+5/5x-10=11 equation: 



7/x-2+5/5x-10=11

We move all terms to the left:

7/x-2+5/5x-10-(11)=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-23=0

We calculate fractions


35x/5x^2+5x/5x^2-23=0

We multiply all the terms by the denominator


35x+5x-23*5x^2=0

We add all the numbers together, and all the variables

40x-23*5x^2=0

Wy multiply elements

-115x^2+40x=0

a = -115; b = 40; c = 0;
Δ = b2-4ac
Δ = 402-4·(-115)·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*-115}=\frac{-80}{-230}
=8/23
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40}{2*-115}=\frac{0}{-230}
=0
$

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