4/x-3=5x

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

4/x-3=5x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-5x+4/x-3=0

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}
$