(x+1)(16x-24)=1

Solution for (x+1)(16x-24)=1 equation:

(x+1)(16x-24)=1

We move all terms to the left:

(x+1)(16x-24)-(1)=0

We multiply parentheses ..

(+16x^2-24x+16x-24)-1=0

We get rid of parentheses

16x^2-24x+16x-24-1=0

We add all the numbers together, and all the variables

16x^2-8x-25=0

a = 16; b = -8; c = -25;
Δ = b2-4ac
Δ = -82-4·16·(-25)
Δ = 1664
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:

$\sqrt{\Delta}=\sqrt{1664}=\sqrt{64*26}=\sqrt{64}*\sqrt{26}=8\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{26}}{2*16}=\frac{8-8\sqrt{26}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{26}}{2*16}=\frac{8+8\sqrt{26}}{32}
$