v^2+6v-46=-3

Solution for v^2+6v-46=-3 equation:

v^2+6v-46=-3

We move all terms to the left:

v^2+6v-46-(-3)=0

We add all the numbers together, and all the variables

v^2+6v-43=0

a = 1; b = 6; c = -43;
Δ = b2-4ac
Δ = 62-4·1·(-43)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{13}}{2*1}=\frac{-6-4\sqrt{13}}{2}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{13}}{2*1}=\frac{-6+4\sqrt{13}}{2}
$