0=4w^2-88w-11

Solution for 0=4w^2-88w-11 equation:

0=4w^2-88w-11

We move all terms to the left:

0-(4w^2-88w-11)=0

We add all the numbers together, and all the variables

-(4w^2-88w-11)=0

We get rid of parentheses

-4w^2+88w+11=0

a = -4; b = 88; c = +11;
Δ = b2-4ac
Δ = 882-4·(-4)·11
Δ = 7920
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:

$\sqrt{\Delta}=\sqrt{7920}=\sqrt{144*55}=\sqrt{144}*\sqrt{55}=12\sqrt{55}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(88)-12\sqrt{55}}{2*-4}=\frac{-88-12\sqrt{55}}{-8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(88)+12\sqrt{55}}{2*-4}=\frac{-88+12\sqrt{55}}{-8}
$