-3(2x+7)=1/2x

Solution for -3(2x+7)=1/2x equation:

-3(2x+7)=1/2x

We move all terms to the left:

-3(2x+7)-(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

-3(2x+7)-(+1/2x)=0

We multiply parentheses

-6x-(+1/2x)-21=0

We get rid of parentheses

-6x-1/2x-21=0

We multiply all the terms by the denominator


-6x*2x-21*2x-1=0

Wy multiply elements

-12x^2-42x-1=0

a = -12; b = -42; c = -1;
Δ = b2-4ac
Δ = -422-4·(-12)·(-1)
Δ = 1716
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:

$\sqrt{\Delta}=\sqrt{1716}=\sqrt{4*429}=\sqrt{4}*\sqrt{429}=2\sqrt{429}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{429}}{2*-12}=\frac{42-2\sqrt{429}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{429}}{2*-12}=\frac{42+2\sqrt{429}}{-24}
$