3(4x+-1)(4x+3)=48x

Solution for 3(4x+-1)(4x+3)=48x equation:

3(4x+-1)(4x+3)=48x

We move all terms to the left:

3(4x+-1)(4x+3)-(48x)=0

We add all the numbers together, and all the variables

3(4x-1)(4x+3)-48x=0

We add all the numbers together, and all the variables

-48x+3(4x-1)(4x+3)=0

We multiply parentheses ..

3(+16x^2+12x-4x-3)-48x=0

We multiply parentheses

48x^2+36x-12x-48x-9=0

We add all the numbers together, and all the variables

48x^2-24x-9=0

a = 48; b = -24; c = -9;
Δ = b2-4ac
Δ = -242-4·48·(-9)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-48}{2*48}=\frac{-24}{96}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+48}{2*48}=\frac{72}{96}
=3/4
$