4x-(80/x)=4

Solution for 4x-(80/x)=4 equation:

4x-(80/x)=4

We move all terms to the left:

4x-(80/x)-(4)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x-(+80/x)-4=0

We get rid of parentheses

4x-80/x-4=0

We multiply all the terms by the denominator


4x*x-4*x-80=0

We add all the numbers together, and all the variables

-4x+4x*x-80=0

Wy multiply elements

4x^2-4x-80=0

a = 4; b = -4; c = -80;
Δ = b2-4ac
Δ = -42-4·4·(-80)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-36}{2*4}=\frac{-32}{8}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+36}{2*4}=\frac{40}{8}
=5
$