x=1/5x-20

Solution for x=1/5x-20 equation:

x=1/5x-20

We move all terms to the left:

x-(1/5x-20)=0


Domain of the equation: 5x-20)!=0

x∈R


We get rid of parentheses

x-1/5x+20=0

We multiply all the terms by the denominator


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

Wy multiply elements

5x^2+100x-1=0

a = 5; b = 100; c = -1;
Δ = b2-4ac
Δ = 1002-4·5·(-1)
Δ = 10020
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:

$\sqrt{\Delta}=\sqrt{10020}=\sqrt{4*2505}=\sqrt{4}*\sqrt{2505}=2\sqrt{2505}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-2\sqrt{2505}}{2*5}=\frac{-100-2\sqrt{2505}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+2\sqrt{2505}}{2*5}=\frac{-100+2\sqrt{2505}}{10}
$