3/8v^2-75=0

Solution for 3/8v^2-75=0 equation:

3/8v^2-75=0


Domain of the equation: 8v^2!=0

v^2!=0/8

v^2!=√0

v!=0

v∈R


We multiply all the terms by the denominator


-75*8v^2+3=0

Wy multiply elements

-600v^2+3=0

a = -600; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-600)·3
Δ = 7200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7200}=\sqrt{3600*2}=\sqrt{3600}*\sqrt{2}=60\sqrt{2}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{2}}{2*-600}=\frac{0-60\sqrt{2}}{-1200}
=-\frac{60\sqrt{2}}{-1200}
=-\frac{\sqrt{2}}{-20}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{2}}{2*-600}=\frac{0+60\sqrt{2}}{-1200}
=\frac{60\sqrt{2}}{-1200}
=\frac{\sqrt{2}}{-20}
$