5x+20/2x-20=6/1

Solution for 5x+20/2x-20=6/1 equation:

5x+20/2x-20=6/1

We move all terms to the left:

5x+20/2x-20-(6/1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

5x+20/2x-20=0

We multiply all the terms by the denominator


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

Wy multiply elements

10x^2-40x+20=0

a = 10; b = -40; c = +20;
Δ = b2-4ac
Δ = -402-4·10·20
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-20\sqrt{2}}{2*10}=\frac{40-20\sqrt{2}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+20\sqrt{2}}{2*10}=\frac{40+20\sqrt{2}}{20}
$