8x(x-1)-5=1

Solution for 8x(x-1)-5=1 equation:

8x(x-1)-5=1

We move all terms to the left:

8x(x-1)-5-(1)=0

We add all the numbers together, and all the variables

8x(x-1)-6=0

We multiply parentheses

8x^2-8x-6=0

a = 8; b = -8; c = -6;
Δ = b2-4ac
Δ = -82-4·8·(-6)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-16}{2*8}=\frac{-8}{16}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16}{2*8}=\frac{24}{16}
=1+1/2
$