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

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

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

We move all terms to the left:

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


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

x∈R


We multiply parentheses

-6x-(1/2x+5)-2=0

We get rid of parentheses

-6x-1/2x-5-2=0

We multiply all the terms by the denominator


-6x*2x-5*2x-2*2x-1=0

Wy multiply elements

-12x^2-10x-4x-1=0

We add all the numbers together, and all the variables

-12x^2-14x-1=0

a = -12; b = -14; c = -1;
Δ = b2-4ac
Δ = -142-4·(-12)·(-1)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{37}}{2*-12}=\frac{14-2\sqrt{37}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{37}}{2*-12}=\frac{14+2\sqrt{37}}{-24}
$