5/3x+7/4x=41/60

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Solution for 5/3x+7/4x=41/60 equation: 



5/3x+7/4x=41/60

We move all terms to the left:

5/3x+7/4x-(41/60)=0



Domain of the equation: 3x!=0

x!=0/3

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

5/3x+7/4x-(+41/60)=0

We get rid of parentheses

5/3x+7/4x-41/60=0

We calculate fractions


(-1968x^2)/4320x^2+7200x/4320x^2+7560x/4320x^2=0

We multiply all the terms by the denominator


(-1968x^2)+7200x+7560x=0

We add all the numbers together, and all the variables

(-1968x^2)+14760x=0

We get rid of parentheses

-1968x^2+14760x=0

a = -1968; b = 14760; c = 0;
Δ = b2-4ac
Δ = 147602-4·(-1968)·0
Δ = 217857600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{217857600}=14760$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14760)-14760}{2*-1968}=\frac{-29520}{-3936}
=7+1/2
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14760)+14760}{2*-1968}=\frac{0}{-3936}
=0
$

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