3v^2-9v-48=-45

Solution for 3v^2-9v-48=-45 equation:

3v^2-9v-48=-45

We move all terms to the left:

3v^2-9v-48-(-45)=0

We add all the numbers together, and all the variables

3v^2-9v-3=0

a = 3; b = -9; c = -3;
Δ = b2-4ac
Δ = -92-4·3·(-3)
Δ = 117
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:

$\sqrt{\Delta}=\sqrt{117}=\sqrt{9*13}=\sqrt{9}*\sqrt{13}=3\sqrt{13}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{13}}{2*3}=\frac{9-3\sqrt{13}}{6}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{13}}{2*3}=\frac{9+3\sqrt{13}}{6}
$