1/5x-20=2x-2

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

1/5x-20=2x-2

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-10x^2-90x+1=0

a = -10; b = -90; c = +1;
Δ = b2-4ac
Δ = -902-4·(-10)·1
Δ = 8140
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:

$\sqrt{\Delta}=\sqrt{8140}=\sqrt{4*2035}=\sqrt{4}*\sqrt{2035}=2\sqrt{2035}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2035}}{2*-10}=\frac{90-2\sqrt{2035}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2035}}{2*-10}=\frac{90+2\sqrt{2035}}{-20}
$