-1=3(w2)-8w

Solution for -1=3(w2)-8w equation:

-1=3(w2)-8w

We move all terms to the left:

-1-(3(w2)-8w)=0

We add all the numbers together, and all the variables

-(+3w^2-8w)-1=0

We get rid of parentheses

-3w^2+8w-1=0

a = -3; b = 8; c = -1;
Δ = b2-4ac
Δ = 82-4·(-3)·(-1)
Δ = 52
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{13}}{2*-3}=\frac{-8-2\sqrt{13}}{-6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{13}}{2*-3}=\frac{-8+2\sqrt{13}}{-6}
$