5w2+23(29-4w2+9)=0

Solution for 5w2+23(29-4w2+9)=0 equation:

5w^2+23(29-4w^2+9)=0

We multiply parentheses

5w^2-92w^2+667+207=0

We add all the numbers together, and all the variables

-87w^2+874=0

a = -87; b = 0; c = +874;
Δ = b2-4ac
Δ = 02-4·(-87)·874
Δ = 304152
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:

$\sqrt{\Delta}=\sqrt{304152}=\sqrt{4*76038}=\sqrt{4}*\sqrt{76038}=2\sqrt{76038}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{76038}}{2*-87}=\frac{0-2\sqrt{76038}}{-174}
=-\frac{2\sqrt{76038}}{-174}
=-\frac{\sqrt{76038}}{-87}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{76038}}{2*-87}=\frac{0+2\sqrt{76038}}{-174}
=\frac{2\sqrt{76038}}{-174}
=\frac{\sqrt{76038}}{-87}
$