(3a-2)(4a-3)=8

Solution for (3a-2)(4a-3)=8 equation:

(3a-2)(4a-3)=8

We move all terms to the left:

(3a-2)(4a-3)-(8)=0

We multiply parentheses ..

(+12a^2-9a-8a+6)-8=0

We get rid of parentheses

12a^2-9a-8a+6-8=0

We add all the numbers together, and all the variables

12a^2-17a-2=0

a = 12; b = -17; c = -2;
Δ = b2-4ac
Δ = -172-4·12·(-2)
Δ = 385
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{385}}{2*12}=\frac{17-\sqrt{385}}{24}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{385}}{2*12}=\frac{17+\sqrt{385}}{24}
$