2v^2=10v+72

Solution for 2v^2=10v+72 equation:

2v^2=10v+72

We move all terms to the left:

2v^2-(10v+72)=0

We get rid of parentheses

2v^2-10v-72=0

a = 2; b = -10; c = -72;
Δ = b2-4ac
Δ = -102-4·2·(-72)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-26}{2*2}=\frac{-16}{4}
=-4
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+26}{2*2}=\frac{36}{4}
=9
$