(8x^2-1)-(4x+22)(-1-2x)-1=0

Solution for (8x^2-1)-(4x+22)(-1-2x)-1=0 equation:

(8x^2-1)-(4x+22)(-1-2x)-1=0

We add all the numbers together, and all the variables

(8x^2-1)-(4x+22)(-2x-1)-1=0

We get rid of parentheses

8x^2-(4x+22)(-2x-1)-1-1=0

We multiply parentheses ..

8x^2-(-8x^2-4x-44x-22)-1-1=0

We add all the numbers together, and all the variables

8x^2-(-8x^2-4x-44x-22)-2=0

We get rid of parentheses

8x^2+8x^2+4x+44x+22-2=0

We add all the numbers together, and all the variables

16x^2+48x+20=0

a = 16; b = 48; c = +20;
Δ = b2-4ac
Δ = 482-4·16·20
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-32}{2*16}=\frac{-80}{32}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+32}{2*16}=\frac{-16}{32}
=-1/2
$