(7+v)(4v+9)=0

Solution for (7+v)(4v+9)=0 equation:

(7+v)(4v+9)=0

We add all the numbers together, and all the variables

(v+7)(4v+9)=0

We multiply parentheses ..

(+4v^2+9v+28v+63)=0

We get rid of parentheses

4v^2+9v+28v+63=0

We add all the numbers together, and all the variables

4v^2+37v+63=0

a = 4; b = 37; c = +63;
Δ = b2-4ac
Δ = 372-4·4·63
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-19}{2*4}=\frac{-56}{8}
=-7
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+19}{2*4}=\frac{-18}{8}
=-2+1/4
$