-1/5x=2x+20

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

-1/5x=2x+20

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-10x^2-100x-1=0

a = -10; b = -100; c = -1;
Δ = b2-4ac
Δ = -1002-4·(-10)·(-1)
Δ = 9960
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:

$\sqrt{\Delta}=\sqrt{9960}=\sqrt{4*2490}=\sqrt{4}*\sqrt{2490}=2\sqrt{2490}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-2\sqrt{2490}}{2*-10}=\frac{100-2\sqrt{2490}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+2\sqrt{2490}}{2*-10}=\frac{100+2\sqrt{2490}}{-20}
$