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

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

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

We add all the numbers together, and all the variables

(4v+7)(-1v+6)=0

We multiply parentheses ..

(-4v^2+24v-7v+42)=0

We get rid of parentheses

-4v^2+24v-7v+42=0

We add all the numbers together, and all the variables

-4v^2+17v+42=0

a = -4; b = 17; c = +42;
Δ = b2-4ac
Δ = 172-4·(-4)·42
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-31}{2*-4}=\frac{-48}{-8}
=+6
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+31}{2*-4}=\frac{14}{-8}
=-1+3/4
$