1/2x+5=2x-1

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

1/2x+5=2x-1

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2+2x+10x+1=0

We add all the numbers together, and all the variables

-4x^2+12x+1=0

a = -4; b = 12; c = +1;
Δ = b2-4ac
Δ = 122-4·(-4)·1
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{10}}{2*-4}=\frac{-12-4\sqrt{10}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{10}}{2*-4}=\frac{-12+4\sqrt{10}}{-8}
$