8(x-6)x=-1

Solution for 8(x-6)x=-1 equation:

8(x-6)x=-1

We move all terms to the left:

8(x-6)x-(-1)=0

We add all the numbers together, and all the variables

8(x-6)x+1=0

We multiply parentheses

8x^2-48x+1=0

a = 8; b = -48; c = +1;
Δ = b2-4ac
Δ = -482-4·8·1
Δ = 2272
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:

$\sqrt{\Delta}=\sqrt{2272}=\sqrt{16*142}=\sqrt{16}*\sqrt{142}=4\sqrt{142}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{142}}{2*8}=\frac{48-4\sqrt{142}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{142}}{2*8}=\frac{48+4\sqrt{142}}{16}
$