5x+2/5x=20

Solution for 5x+2/5x=20 equation:

5x+2/5x=20

We move all terms to the left:

5x+2/5x-(20)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

25x^2-100x+2=0

a = 25; b = -100; c = +2;
Δ = b2-4ac
Δ = -1002-4·25·2
Δ = 9800
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:

$\sqrt{\Delta}=\sqrt{9800}=\sqrt{4900*2}=\sqrt{4900}*\sqrt{2}=70\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-70\sqrt{2}}{2*25}=\frac{100-70\sqrt{2}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+70\sqrt{2}}{2*25}=\frac{100+70\sqrt{2}}{50}
$