-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}
$