5v(v+1)=45+5v

Solution for 5v(v+1)=45+5v equation:

5v(v+1)=45+5v

We move all terms to the left:

5v(v+1)-(45+5v)=0

We add all the numbers together, and all the variables

5v(v+1)-(5v+45)=0

We multiply parentheses

5v^2+5v-(5v+45)=0

We get rid of parentheses

5v^2+5v-5v-45=0

We add all the numbers together, and all the variables

5v^2-45=0

a = 5; b = 0; c = -45;
Δ = b2-4ac
Δ = 02-4·5·(-45)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30}{2*5}=\frac{-30}{10}
=-3
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30}{2*5}=\frac{30}{10}
=3
$