w^2+0.75w^2=20^2

Solution for w^2+0.75w^2=20^2 equation:

w^2+0.75w^2=20^2

We move all terms to the left:

w^2+0.75w^2-(20^2)=0

We add all the numbers together, and all the variables

1.75w^2-400=0

a = 1.75; b = 0; c = -400;
Δ = b2-4ac
Δ = 02-4·1.75·(-400)
Δ = 2800
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:

$\sqrt{\Delta}=\sqrt{2800}=\sqrt{400*7}=\sqrt{400}*\sqrt{7}=20\sqrt{7}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{7}}{2*1.75}=\frac{0-20\sqrt{7}}{3.5}
=-\frac{20\sqrt{7}}{3.5}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{7}}{2*1.75}=\frac{0+20\sqrt{7}}{3.5}
=\frac{20\sqrt{7}}{3.5}
$