w^2+0.75w^2=34^2

Solution for w^2+0.75w^2=34^2 equation:

w^2+0.75w^2=34^2

We move all terms to the left:

w^2+0.75w^2-(34^2)=0

We add all the numbers together, and all the variables

1.75w^2-1156=0

a = 1.75; b = 0; c = -1156;
Δ = b2-4ac
Δ = 02-4·1.75·(-1156)
Δ = 8092
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:

$\sqrt{\Delta}=\sqrt{8092}=\sqrt{1156*7}=\sqrt{1156}*\sqrt{7}=34\sqrt{7}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-34\sqrt{7}}{2*1.75}=\frac{0-34\sqrt{7}}{3.5}
=-\frac{34\sqrt{7}}{3.5}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+34\sqrt{7}}{2*1.75}=\frac{0+34\sqrt{7}}{3.5}
=\frac{34\sqrt{7}}{3.5}
$