5/3x-3/4x=-121/84

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Solution for 5/3x-3/4x=-121/84 equation: 



5/3x-3/4x=-121/84

We move all terms to the left:

5/3x-3/4x-(-121/84)=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 get rid of parentheses

5/3x-3/4x+121/84=0

We calculate fractions


5808x^2/8064x^2+13440x/8064x^2+(-6048x)/8064x^2=0

We multiply all the terms by the denominator


5808x^2+13440x+(-6048x)=0

We get rid of parentheses

5808x^2+13440x-6048x=0

We add all the numbers together, and all the variables

5808x^2+7392x=0

a = 5808; b = 7392; c = 0;
Δ = b2-4ac
Δ = 73922-4·5808·0
Δ = 54641664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{54641664}=7392$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7392)-7392}{2*5808}=\frac{-14784}{11616}
=-1+3/11
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7392)+7392}{2*5808}=\frac{0}{11616}
=0
$

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