1/5x+6=3/4x=

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Solution for 1/5x+6=3/4x= equation: 



1/5x+6=3/4x=

We move all terms to the left:

1/5x+6-(3/4x)=0



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R





Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R



We add all the numbers together, and all the variables

1/5x-(+3/4x)+6=0

We get rid of parentheses

1/5x-3/4x+6=0

We calculate fractions


4x/20x^2+(-15x)/20x^2+6=0

We multiply all the terms by the denominator


4x+(-15x)+6*20x^2=0

Wy multiply elements

120x^2+4x+(-15x)=0

We get rid of parentheses

120x^2+4x-15x=0

We add all the numbers together, and all the variables

120x^2-11x=0

a = 120; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·120·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*120}=\frac{0}{240}
=0
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*120}=\frac{22}{240}
=11/120
$

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