12v^2-51v-45=0

Solution for 12v^2-51v-45=0 equation:

12v^2-51v-45=0

a = 12; b = -51; c = -45;
Δ = b2-4ac
Δ = -512-4·12·(-45)
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-69}{2*12}=\frac{-18}{24}
=-3/4
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+69}{2*12}=\frac{120}{24}
=5
$