2v^2+4=49

Solution for 2v^2+4=49 equation:

2v^2+4=49

We move all terms to the left:

2v^2+4-(49)=0

We add all the numbers together, and all the variables

2v^2-45=0

a = 2; b = 0; c = -45;
Δ = b2-4ac
Δ = 02-4·2·(-45)
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{10}}{2*2}=\frac{0-6\sqrt{10}}{4}
=-\frac{6\sqrt{10}}{4}
=-\frac{3\sqrt{10}}{2}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{10}}{2*2}=\frac{0+6\sqrt{10}}{4}
=\frac{6\sqrt{10}}{4}
=\frac{3\sqrt{10}}{2}
$