((3x-8)12x)=1

Solution for ((3x-8)12x)=1 equation:

((3x-8)12x)=1

We move all terms to the left:

((3x-8)12x)-(1)=0


We calculate terms in parentheses: +((3x-8)12x), so:

(3x-8)12x

We multiply parentheses

36x^2-96x

Back to the equation:

+(36x^2-96x)


We get rid of parentheses

36x^2-96x-1=0

a = 36; b = -96; c = -1;
Δ = b2-4ac
Δ = -962-4·36·(-1)
Δ = 9360
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9360}=\sqrt{144*65}=\sqrt{144}*\sqrt{65}=12\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-12\sqrt{65}}{2*36}=\frac{96-12\sqrt{65}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+12\sqrt{65}}{2*36}=\frac{96+12\sqrt{65}}{72}
$