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

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

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

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

-4x-(+1/2x)-10=0

We get rid of parentheses

-4x-1/2x-10=0

We multiply all the terms by the denominator


-4x*2x-10*2x-1=0

Wy multiply elements

-8x^2-20x-1=0

a = -8; b = -20; c = -1;
Δ = b2-4ac
Δ = -202-4·(-8)·(-1)
Δ = 368
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:

$\sqrt{\Delta}=\sqrt{368}=\sqrt{16*23}=\sqrt{16}*\sqrt{23}=4\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{23}}{2*-8}=\frac{20-4\sqrt{23}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{23}}{2*-8}=\frac{20+4\sqrt{23}}{-16}
$