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

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

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

We move all terms to the left:

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

We multiply parentheses ..

4(+x^2-3x+4x-12)-1=0

We multiply parentheses

4x^2-12x+16x-48-1=0

We add all the numbers together, and all the variables

4x^2+4x-49=0

a = 4; b = 4; c = -49;
Δ = b2-4ac
Δ = 42-4·4·(-49)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-20\sqrt{2}}{2*4}=\frac{-4-20\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+20\sqrt{2}}{2*4}=\frac{-4+20\sqrt{2}}{8}
$