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

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

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

We move all terms to the left:

1/5x+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

-1x+1/5x+2/5x+20=0

We multiply all the terms by the denominator


-1x*5x+20*5x+1+2=0

We add all the numbers together, and all the variables

-1x*5x+20*5x+3=0

Wy multiply elements

-5x^2+100x+3=0

a = -5; b = 100; c = +3;
Δ = b2-4ac
Δ = 1002-4·(-5)·3
Δ = 10060
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:

$\sqrt{\Delta}=\sqrt{10060}=\sqrt{4*2515}=\sqrt{4}*\sqrt{2515}=2\sqrt{2515}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-2\sqrt{2515}}{2*-5}=\frac{-100-2\sqrt{2515}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+2\sqrt{2515}}{2*-5}=\frac{-100+2\sqrt{2515}}{-10}
$