1/4x+1/5x-3=15

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Solution for 1/4x+1/5x-3=15 equation:



1/4x+1/5x-3=15
We move all terms to the left:
1/4x+1/5x-3-(15)=0
Domain of the equation: 4x!=0
x!=0/4
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
1/4x+1/5x-18=0
We calculate fractions
5x/20x^2+4x/20x^2-18=0
We multiply all the terms by the denominator
5x+4x-18*20x^2=0
We add all the numbers together, and all the variables
9x-18*20x^2=0
Wy multiply elements
-360x^2+9x=0
a = -360; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-360)·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*-360}=\frac{-18}{-720} =1/40 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-360}=\frac{0}{-720} =0 $

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