4/x=5x-8

Solution for 4/x=5x-8 equation:

4/x=5x-8

We move all terms to the left:

4/x-(5x-8)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

4/x-5x+8=0

We multiply all the terms by the denominator


-5x*x+8*x+4=0

We add all the numbers together, and all the variables

8x-5x*x+4=0

Wy multiply elements

-5x^2+8x+4=0

a = -5; b = 8; c = +4;
Δ = b2-4ac
Δ = 82-4·(-5)·4
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-12}{2*-5}=\frac{-20}{-10}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12}{2*-5}=\frac{4}{-10}
=-2/5
$