v(v-3)=-7-10v

Solution for v(v-3)=-7-10v equation:

v(v-3)=-7-10v

We move all terms to the left:

v(v-3)-(-7-10v)=0

We add all the numbers together, and all the variables

v(v-3)-(-10v-7)=0

We multiply parentheses

v^2-3v-(-10v-7)=0

We get rid of parentheses

v^2-3v+10v+7=0

We add all the numbers together, and all the variables

v^2+7v+7=0

a = 1; b = 7; c = +7;
Δ = b2-4ac
Δ = 72-4·1·7
Δ = 21
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{21}}{2*1}=\frac{-7-\sqrt{21}}{2}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{21}}{2*1}=\frac{-7+\sqrt{21}}{2}
$