-3x-(-12)=-24-1/2x

Solution for -3x-(-12)=-24-1/2x equation:

-3x-(-12)=-24-1/2x

We move all terms to the left:

-3x-(-12)-(-24-1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-3x-(-1/2x-24)-(-12)=0

We add all the numbers together, and all the variables

-3x-(-1/2x-24)+12=0

We get rid of parentheses

-3x+1/2x+24+12=0

We multiply all the terms by the denominator


-3x*2x+24*2x+12*2x+1=0

Wy multiply elements

-6x^2+48x+24x+1=0

We add all the numbers together, and all the variables

-6x^2+72x+1=0

a = -6; b = 72; c = +1;
Δ = b2-4ac
Δ = 722-4·(-6)·1
Δ = 5208
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:

$\sqrt{\Delta}=\sqrt{5208}=\sqrt{4*1302}=\sqrt{4}*\sqrt{1302}=2\sqrt{1302}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-2\sqrt{1302}}{2*-6}=\frac{-72-2\sqrt{1302}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+2\sqrt{1302}}{2*-6}=\frac{-72+2\sqrt{1302}}{-12}
$