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

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

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

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

12x^2-2x-2=0

a = 12; b = -2; c = -2;
Δ = b2-4ac
Δ = -22-4·12·(-2)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10}{2*12}=\frac{-8}{24}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*12}=\frac{12}{24}
=1/2
$