w(3w+23w)=8

Solution for w(3w+23w)=8 equation:

w(3w+23w)=8

We move all terms to the left:

w(3w+23w)-(8)=0

We add all the numbers together, and all the variables

w(+26w)-8=0

We multiply parentheses

26w^2-8=0

a = 26; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·26·(-8)
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{13}}{2*26}=\frac{0-8\sqrt{13}}{52}
=-\frac{8\sqrt{13}}{52}
=-\frac{2\sqrt{13}}{13}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{13}}{2*26}=\frac{0+8\sqrt{13}}{52}
=\frac{8\sqrt{13}}{52}
=\frac{2\sqrt{13}}{13}
$