8/5w^2=160

Solution for 8/5w^2=160 equation:

8/5w^2=160

We move all terms to the left:

8/5w^2-(160)=0


Domain of the equation: 5w^2!=0

w^2!=0/5

w^2!=√0

w!=0

w∈R


We multiply all the terms by the denominator


-160*5w^2+8=0

Wy multiply elements

-800w^2+8=0

a = -800; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-800)·8
Δ = 25600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25600}=160$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-160}{2*-800}=\frac{-160}{-1600}
=1/10
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+160}{2*-800}=\frac{160}{-1600}
=-1/10
$