5x+4=20/5x+4

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

5x+4=20/5x+4

We move all terms to the left:

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


Domain of the equation: 5x+4)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

25x^2-20x+20x-20=0

We add all the numbers together, and all the variables

25x^2-20=0

a = 25; b = 0; c = -20;
Δ = b2-4ac
Δ = 02-4·25·(-20)
Δ = 2000
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:

$\sqrt{\Delta}=\sqrt{2000}=\sqrt{400*5}=\sqrt{400}*\sqrt{5}=20\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{5}}{2*25}=\frac{0-20\sqrt{5}}{50}
=-\frac{20\sqrt{5}}{50}
=-\frac{2\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{5}}{2*25}=\frac{0+20\sqrt{5}}{50}
=\frac{20\sqrt{5}}{50}
=\frac{2\sqrt{5}}{5}
$