8=1/2(1960)x^2

Solution for 8=1/2(1960)x^2 equation:

8=1/2(1960)x^2

We move all terms to the left:

8-(1/2(1960)x^2)=0


Domain of the equation: 21960x^2)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-1/21960x^2+8=0

We multiply all the terms by the denominator


8*21960x^2-1=0

Wy multiply elements

175680x^2-1=0

a = 175680; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·175680·(-1)
Δ = 702720
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:

$\sqrt{\Delta}=\sqrt{702720}=\sqrt{2304*305}=\sqrt{2304}*\sqrt{305}=48\sqrt{305}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{305}}{2*175680}=\frac{0-48\sqrt{305}}{351360}
=-\frac{48\sqrt{305}}{351360}
=-\frac{\sqrt{305}}{7320}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{305}}{2*175680}=\frac{0+48\sqrt{305}}{351360}
=\frac{48\sqrt{305}}{351360}
=\frac{\sqrt{305}}{7320}
$