5x+4=1/5x+8

Solution for 5x+4=1/5x+8 equation:

5x+4=1/5x+8

We move all terms to the left:

5x+4-(1/5x+8)=0


Domain of the equation: 5x+8)!=0

x∈R


We get rid of parentheses

5x-1/5x-8+4=0

We multiply all the terms by the denominator


5x*5x-8*5x+4*5x-1=0

Wy multiply elements

25x^2-40x+20x-1=0

We add all the numbers together, and all the variables

25x^2-20x-1=0

a = 25; b = -20; c = -1;
Δ = b2-4ac
Δ = -202-4·25·(-1)
Δ = 500
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:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-10\sqrt{5}}{2*25}=\frac{20-10\sqrt{5}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+10\sqrt{5}}{2*25}=\frac{20+10\sqrt{5}}{50}
$