(4v+6)(7+v)=0

Solution for (4v+6)(7+v)=0 equation:

(4v+6)(7+v)=0

We add all the numbers together, and all the variables

(4v+6)(v+7)=0

We multiply parentheses ..

(+4v^2+28v+6v+42)=0

We get rid of parentheses

4v^2+28v+6v+42=0

We add all the numbers together, and all the variables

4v^2+34v+42=0

a = 4; b = 34; c = +42;
Δ = b2-4ac
Δ = 342-4·4·42
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-22}{2*4}=\frac{-56}{8}
=-7
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+22}{2*4}=\frac{-12}{8}
=-1+1/2
$