30v^2-114=0

Solution for 30v^2-114=0 equation:

30v^2-114=0

a = 30; b = 0; c = -114;
Δ = b2-4ac
Δ = 02-4·30·(-114)
Δ = 13680
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:

$\sqrt{\Delta}=\sqrt{13680}=\sqrt{144*95}=\sqrt{144}*\sqrt{95}=12\sqrt{95}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{95}}{2*30}=\frac{0-12\sqrt{95}}{60}
=-\frac{12\sqrt{95}}{60}
=-\frac{\sqrt{95}}{5}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{95}}{2*30}=\frac{0+12\sqrt{95}}{60}
=\frac{12\sqrt{95}}{60}
=\frac{\sqrt{95}}{5}
$