5x-20/3x=1

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Solution for 5x-20/3x=1 equation: 



5x-20/3x=1

We move all terms to the left:

5x-20/3x-(1)=0



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



We multiply all the terms by the denominator


5x*3x-1*3x-20=0

Wy multiply elements

15x^2-3x-20=0

a = 15; b = -3; c = -20;
Δ = b2-4ac
Δ = -32-4·15·(-20)
Δ = 1209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{1209}}{2*15}=\frac{3-\sqrt{1209}}{30}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{1209}}{2*15}=\frac{3+\sqrt{1209}}{30}
$

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