(v-3)=(v^2+8v)

Solution for (v-3)=(v^2+8v) equation:

(v-3)=(v^2+8v)

We move all terms to the left:

(v-3)-((v^2+8v))=0

We get rid of parentheses

v-((v^2+8v))-3=0


We calculate terms in parentheses: -((v^2+8v)), so:

(v^2+8v)

We get rid of parentheses

v^2+8v

Back to the equation:

-(v^2+8v)


We get rid of parentheses

-v^2+v-8v-3=0

We add all the numbers together, and all the variables

-1v^2-7v-3=0

a = -1; b = -7; c = -3;
Δ = b2-4ac
Δ = -72-4·(-1)·(-3)
Δ = 37
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{37}}{2*-1}=\frac{7-\sqrt{37}}{-2}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{37}}{2*-1}=\frac{7+\sqrt{37}}{-2}
$