-1/2x+1=x-5

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

-1/2x+1=x-5

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-2x^2+12x-1=0

a = -2; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·(-2)·(-1)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{34}}{2*-2}=\frac{-12-2\sqrt{34}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{34}}{2*-2}=\frac{-12+2\sqrt{34}}{-4}
$