2x+6+4x+2/5x-20=x

Solution for 2x+6+4x+2/5x-20=x equation:

2x+6+4x+2/5x-20=x

We move all terms to the left:

2x+6+4x+2/5x-20-(x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

5x+2/5x-14=0

We multiply all the terms by the denominator


5x*5x-14*5x+2=0

Wy multiply elements

25x^2-70x+2=0

a = 25; b = -70; c = +2;
Δ = b2-4ac
Δ = -702-4·25·2
Δ = 4700
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:

$\sqrt{\Delta}=\sqrt{4700}=\sqrt{100*47}=\sqrt{100}*\sqrt{47}=10\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-10\sqrt{47}}{2*25}=\frac{70-10\sqrt{47}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+10\sqrt{47}}{2*25}=\frac{70+10\sqrt{47}}{50}
$