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

Solution for (5/x)-4=4x-5 equation:

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

We move all terms to the left:

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


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

5/x-4x+5-4=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x-4x*x+5=0

Wy multiply elements

-4x^2+x+5=0

a = -4; b = 1; c = +5;
Δ = b2-4ac
Δ = 12-4·(-4)·5
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-9}{2*-4}=\frac{-10}{-8}
=1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+9}{2*-4}=\frac{8}{-8}
=-1
$