-2(3x+1)=1-1/2x+5

Solution for -2(3x+1)=1-1/2x+5 equation:

-2(3x+1)=1-1/2x+5

We move all terms to the left:

-2(3x+1)-(1-1/2x+5)=0


Domain of the equation: 2x+5)!=0

x∈R


We add all the numbers together, and all the variables

-2(3x+1)-(-1/2x+6)=0

We multiply parentheses

-6x-(-1/2x+6)-2=0

We get rid of parentheses

-6x+1/2x-6-2=0

We multiply all the terms by the denominator


-6x*2x-6*2x-2*2x+1=0

Wy multiply elements

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

We add all the numbers together, and all the variables

-12x^2-16x+1=0

a = -12; b = -16; c = +1;
Δ = b2-4ac
Δ = -162-4·(-12)·1
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{19}}{2*-12}=\frac{16-4\sqrt{19}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{19}}{2*-12}=\frac{16+4\sqrt{19}}{-24}
$