5v^2+8v=12

Solution for 5v^2+8v=12 equation:

5v^2+8v=12

We move all terms to the left:

5v^2+8v-(12)=0

a = 5; b = 8; c = -12;
Δ = b2-4ac
Δ = 82-4·5·(-12)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{19}}{2*5}=\frac{-8-4\sqrt{19}}{10}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{19}}{2*5}=\frac{-8+4\sqrt{19}}{10}
$