3/160x^2=42

Solution for 3/160x^2=42 equation:

3/160x^2=42

We move all terms to the left:

3/160x^2-(42)=0


Domain of the equation: 160x^2!=0

x^2!=0/160

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-42*160x^2+3=0

Wy multiply elements

-6720x^2+3=0

a = -6720; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-6720)·3
Δ = 80640
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{80640}=\sqrt{2304*35}=\sqrt{2304}*\sqrt{35}=48\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{35}}{2*-6720}=\frac{0-48\sqrt{35}}{-13440}
=-\frac{48\sqrt{35}}{-13440}
=-\frac{\sqrt{35}}{-280}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{35}}{2*-6720}=\frac{0+48\sqrt{35}}{-13440}
=\frac{48\sqrt{35}}{-13440}
=\frac{\sqrt{35}}{-280}
$