(4a)=2(4a)^2-3(4a)

Solution for (4a)=2(4a)^2-3(4a) equation:

(4a)=2(4a)^2-3(4a)

We move all terms to the left:

(4a)-(2(4a)^2-3(4a))=0

We get rid of parentheses

-24a^2+4a+34a=0

We add all the numbers together, and all the variables

-24a^2+38a=0

a = -24; b = 38; c = 0;
Δ = b2-4ac
Δ = 382-4·(-24)·0
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-38}{2*-24}=\frac{-76}{-48}
=1+7/12
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+38}{2*-24}=\frac{0}{-48}
=0
$