3a-12=1/2a-7

Solution for 3a-12=1/2a-7 equation:

3a-12=1/2a-7

We move all terms to the left:

3a-12-(1/2a-7)=0


Domain of the equation: 2a-7)!=0

a∈R


We get rid of parentheses

3a-1/2a+7-12=0

We multiply all the terms by the denominator


3a*2a+7*2a-12*2a-1=0

Wy multiply elements

6a^2+14a-24a-1=0

We add all the numbers together, and all the variables

6a^2-10a-1=0

a = 6; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·6·(-1)
Δ = 124
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{31}}{2*6}=\frac{10-2\sqrt{31}}{12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{31}}{2*6}=\frac{10+2\sqrt{31}}{12}
$