(4v+8)(7v+2)=9

Solution for (4v+8)(7v+2)=9 equation:

(4v+8)(7v+2)=9

We move all terms to the left:

(4v+8)(7v+2)-(9)=0

We multiply parentheses ..

(+28v^2+8v+56v+16)-9=0

We get rid of parentheses

28v^2+8v+56v+16-9=0

We add all the numbers together, and all the variables

28v^2+64v+7=0

a = 28; b = 64; c = +7;
Δ = b2-4ac
Δ = 642-4·28·7
Δ = 3312
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3312}=\sqrt{144*23}=\sqrt{144}*\sqrt{23}=12\sqrt{23}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-12\sqrt{23}}{2*28}=\frac{-64-12\sqrt{23}}{56}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+12\sqrt{23}}{2*28}=\frac{-64+12\sqrt{23}}{56}
$