4(5a-8)2a=12a-6

Solution for 4(5a-8)2a=12a-6 equation:

4(5a-8)2a=12a-6

We move all terms to the left:

4(5a-8)2a-(12a-6)=0

We multiply parentheses

40a^2-64a-(12a-6)=0

We get rid of parentheses

40a^2-64a-12a+6=0

We add all the numbers together, and all the variables

40a^2-76a+6=0

a = 40; b = -76; c = +6;
Δ = b2-4ac
Δ = -762-4·40·6
Δ = 4816
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:

$\sqrt{\Delta}=\sqrt{4816}=\sqrt{16*301}=\sqrt{16}*\sqrt{301}=4\sqrt{301}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-4\sqrt{301}}{2*40}=\frac{76-4\sqrt{301}}{80}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+4\sqrt{301}}{2*40}=\frac{76+4\sqrt{301}}{80}
$