45=1/2(10)(v^2)

Solution for 45=1/2(10)(v^2) equation:

45=1/2(10)(v^2)

We move all terms to the left:

45-(1/2(10)(v^2))=0


Domain of the equation: 210v^2)!=0

v!=0/1

v!=0

v∈R


We get rid of parentheses

-1/210v^2+45=0

We multiply all the terms by the denominator


45*210v^2-1=0

Wy multiply elements

9450v^2-1=0

a = 9450; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·9450·(-1)
Δ = 37800
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:

$\sqrt{\Delta}=\sqrt{37800}=\sqrt{900*42}=\sqrt{900}*\sqrt{42}=30\sqrt{42}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{42}}{2*9450}=\frac{0-30\sqrt{42}}{18900}
=-\frac{30\sqrt{42}}{18900}
=-\frac{\sqrt{42}}{630}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{42}}{2*9450}=\frac{0+30\sqrt{42}}{18900}
=\frac{30\sqrt{42}}{18900}
=\frac{\sqrt{42}}{630}
$