5x-4/x=3

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

5x-4/x=3

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


5x*x-3*x-4=0

We add all the numbers together, and all the variables

-3x+5x*x-4=0

Wy multiply elements

5x^2-3x-4=0

a = 5; b = -3; c = -4;
Δ = b2-4ac
Δ = -32-4·5·(-4)
Δ = 89
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{89}}{2*5}=\frac{3-\sqrt{89}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{89}}{2*5}=\frac{3+\sqrt{89}}{10}
$