90=1/25v2

Solution for 90=1/25v2 equation:

90=1/25v^2

We move all terms to the left:

90-(1/25v^2)=0


Domain of the equation: 25v^2)!=0

v!=0/1

v!=0

v∈R


We get rid of parentheses

-1/25v^2+90=0

We multiply all the terms by the denominator


90*25v^2-1=0

Wy multiply elements

2250v^2-1=0

a = 2250; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·2250·(-1)
Δ = 9000
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:

$\sqrt{\Delta}=\sqrt{9000}=\sqrt{900*10}=\sqrt{900}*\sqrt{10}=30\sqrt{10}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{10}}{2*2250}=\frac{0-30\sqrt{10}}{4500}
=-\frac{30\sqrt{10}}{4500}
=-\frac{\sqrt{10}}{150}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{10}}{2*2250}=\frac{0+30\sqrt{10}}{4500}
=\frac{30\sqrt{10}}{4500}
=\frac{\sqrt{10}}{150}
$