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

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



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

We move all terms to the left:

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



Domain of the equation: x!=0

x∈R



We add all the numbers together, and all the variables

3x-5/x-5-0=0

We add all the numbers together, and all the variables

3x-5/x-5=0

We multiply all the terms by the denominator


3x*x-5*x-5=0

We add all the numbers together, and all the variables

-5x+3x*x-5=0

Wy multiply elements

3x^2-5x-5=0

a = 3; b = -5; c = -5;
Δ = b2-4ac
Δ = -52-4·3·(-5)
Δ = 85
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{-(-5)-\sqrt{85}}{2*3}=\frac{5-\sqrt{85}}{6}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{85}}{2*3}=\frac{5+\sqrt{85}}{6}
$

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