1/5x+1+1/4x=11

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Solution for 1/5x+1+1/4x=11 equation:



1/5x+1+1/4x=11
We move all terms to the left:
1/5x+1+1/4x-(11)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
We add all the numbers together, and all the variables
1/5x+1/4x-10=0
We calculate fractions
4x/20x^2+5x/20x^2-10=0
We multiply all the terms by the denominator
4x+5x-10*20x^2=0
We add all the numbers together, and all the variables
9x-10*20x^2=0
Wy multiply elements
-200x^2+9x=0
a = -200; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-200)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-200}=\frac{-18}{-400} =9/200 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-200}=\frac{0}{-400} =0 $

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