1/5x-50=2x-5

Solution for 1/5x-50=2x-5 equation:

1/5x-50=2x-5

We move all terms to the left:

1/5x-50-(2x-5)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

1/5x-2x+5-50=0

We multiply all the terms by the denominator


-2x*5x+5*5x-50*5x+1=0

Wy multiply elements

-10x^2+25x-250x+1=0

We add all the numbers together, and all the variables

-10x^2-225x+1=0

a = -10; b = -225; c = +1;
Δ = b2-4ac
Δ = -2252-4·(-10)·1
Δ = 50665
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-225)-\sqrt{50665}}{2*-10}=\frac{225-\sqrt{50665}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-225)+\sqrt{50665}}{2*-10}=\frac{225+\sqrt{50665}}{-20}
$