4v^2-24v-21=0

Solution for 4v^2-24v-21=0 equation:

4v^2-24v-21=0

a = 4; b = -24; c = -21;
Δ = b2-4ac
Δ = -242-4·4·(-21)
Δ = 912
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:

$\sqrt{\Delta}=\sqrt{912}=\sqrt{16*57}=\sqrt{16}*\sqrt{57}=4\sqrt{57}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{57}}{2*4}=\frac{24-4\sqrt{57}}{8}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{57}}{2*4}=\frac{24+4\sqrt{57}}{8}
$