6(2v-3)v=5

Solution for 6(2v-3)v=5 equation:

6(2v-3)v=5

We move all terms to the left:

6(2v-3)v-(5)=0

We multiply parentheses

12v^2-18v-5=0

a = 12; b = -18; c = -5;
Δ = b2-4ac
Δ = -182-4·12·(-5)
Δ = 564
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:

$\sqrt{\Delta}=\sqrt{564}=\sqrt{4*141}=\sqrt{4}*\sqrt{141}=2\sqrt{141}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{141}}{2*12}=\frac{18-2\sqrt{141}}{24}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{141}}{2*12}=\frac{18+2\sqrt{141}}{24}
$