/6a-8=4a+6

Solution for /6a-8=4a+6 equation:

/6a-8=4a+6

We move all terms to the left:

/6a-8-(4a+6)=0


Domain of the equation: 6a!=0

a!=0/6

a!=0

a∈R


We get rid of parentheses

/6a-4a-6-8=0

We multiply all the terms by the denominator


-4a*6a-6*6a-8*6a+=0

We add all the numbers together, and all the variables

-4a*6a-6*6a-8*6a=0

Wy multiply elements

-24a^2-36a-48a=0

We add all the numbers together, and all the variables

-24a^2-84a=0

a = -24; b = -84; c = 0;
Δ = b2-4ac
Δ = -842-4·(-24)·0
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-84}{2*-24}=\frac{0}{-48}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+84}{2*-24}=\frac{168}{-48}
=-3+1/2
$