(3v+5)(7-v)=0

Solution for (3v+5)(7-v)=0 equation:

(3v+5)(7-v)=0

We add all the numbers together, and all the variables

(3v+5)(-1v+7)=0

We multiply parentheses ..

(-3v^2+21v-5v+35)=0

We get rid of parentheses

-3v^2+21v-5v+35=0

We add all the numbers together, and all the variables

-3v^2+16v+35=0

a = -3; b = 16; c = +35;
Δ = b2-4ac
Δ = 162-4·(-3)·35
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-26}{2*-3}=\frac{-42}{-6}
=+7
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+26}{2*-3}=\frac{10}{-6}
=-1+2/3
$