20+5x=1/4x

Solution for 20+5x=1/4x equation:

20+5x=1/4x

We move all terms to the left:

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


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

5x-1/4x+20=0

We multiply all the terms by the denominator


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

Wy multiply elements

20x^2+80x-1=0

a = 20; b = 80; c = -1;
Δ = b2-4ac
Δ = 802-4·20·(-1)
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*20}=\frac{-80-36\sqrt{5}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+36\sqrt{5}}{2*20}=\frac{-80+36\sqrt{5}}{40}
$