5-1/x-4=5x-21/x-4

Solution for 5-1/x-4=5x-21/x-4 equation:

5-1/x-4=5x-21/x-4

We move all terms to the left:

5-1/x-4-(5x-21/x-4)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x-4)!=0

x∈R


We add all the numbers together, and all the variables

-1/x-(5x-21/x-4)+1=0

We get rid of parentheses

-1/x-5x+21/x+4+1=0

We multiply all the terms by the denominator


-5x*x+4*x+1*x-1+21=0

We add all the numbers together, and all the variables

5x-5x*x+20=0

Wy multiply elements

-5x^2+5x+20=0

a = -5; b = 5; c = +20;
Δ = b2-4ac
Δ = 52-4·(-5)·20
Δ = 425
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{17}}{2*-5}=\frac{-5-5\sqrt{17}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{17}}{2*-5}=\frac{-5+5\sqrt{17}}{-10}
$