6a(-2+4)+6=4a+54

Solution for 6a(-2+4)+6=4a+54 equation:

6a(-2+4)+6=4a+54

We move all terms to the left:

6a(-2+4)+6-(4a+54)=0

We add all the numbers together, and all the variables

6a2-(4a+54)+6=0

We add all the numbers together, and all the variables

6a^2-(4a+54)+6=0

We get rid of parentheses

6a^2-4a-54+6=0

We add all the numbers together, and all the variables

6a^2-4a-48=0

a = 6; b = -4; c = -48;
Δ = b2-4ac
Δ = -42-4·6·(-48)
Δ = 1168
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:

$\sqrt{\Delta}=\sqrt{1168}=\sqrt{16*73}=\sqrt{16}*\sqrt{73}=4\sqrt{73}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{73}}{2*6}=\frac{4-4\sqrt{73}}{12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{73}}{2*6}=\frac{4+4\sqrt{73}}{12}
$