5/4x+20=x

Solution for 5/4x+20=x equation:

5/4x+20=x

We move all terms to the left:

5/4x+20-(x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+5/4x+20=0

We multiply all the terms by the denominator


-1x*4x+20*4x+5=0

Wy multiply elements

-4x^2+80x+5=0

a = -4; b = 80; c = +5;
Δ = b2-4ac
Δ = 802-4·(-4)·5
Δ = 6480
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:

$\sqrt{\Delta}=\sqrt{6480}=\sqrt{1296*5}=\sqrt{1296}*\sqrt{5}=36\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-36\sqrt{5}}{2*-4}=\frac{-80-36\sqrt{5}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+36\sqrt{5}}{2*-4}=\frac{-80+36\sqrt{5}}{-8}
$