13(6x-12)=4(1/2x+1)-2

Solution for 13(6x-12)=4(1/2x+1)-2 equation:

13(6x-12)=4(1/2x+1)-2

We move all terms to the left:

13(6x-12)-(4(1/2x+1)-2)=0


Domain of the equation: 2x+1)-2)!=0

x∈R


We multiply parentheses

78x-(4(1/2x+1)-2)-156=0

We multiply all the terms by the denominator


78x*2x-156*2x+1)-2)-(4(1+1)-2)=0

We add all the numbers together, and all the variables

78x*2x-156*2x+1)-2)-(42-2)=0

We add all the numbers together, and all the variables

78x*2x-156*2x=0

Wy multiply elements

156x^2-312x=0

a = 156; b = -312; c = 0;
Δ = b2-4ac
Δ = -3122-4·156·0
Δ = 97344
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{97344}=312$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-312)-312}{2*156}=\frac{0}{312}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-312)+312}{2*156}=\frac{624}{312}
=2
$