7v^2+2=492

Solution for 7v^2+2=492 equation:

7v^2+2=492

We move all terms to the left:

7v^2+2-(492)=0

We add all the numbers together, and all the variables

7v^2-490=0

a = 7; b = 0; c = -490;
Δ = b2-4ac
Δ = 02-4·7·(-490)
Δ = 13720
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:

$\sqrt{\Delta}=\sqrt{13720}=\sqrt{196*70}=\sqrt{196}*\sqrt{70}=14\sqrt{70}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{70}}{2*7}=\frac{0-14\sqrt{70}}{14}
=-\frac{14\sqrt{70}}{14}
=-\sqrt{70}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{70}}{2*7}=\frac{0+14\sqrt{70}}{14}
=\frac{14\sqrt{70}}{14}
=\sqrt{70}
$