(7v+9)(6v+7)=0

Solution for (7v+9)(6v+7)=0 equation:

(7v+9)(6v+7)=0

We multiply parentheses ..

(+42v^2+49v+54v+63)=0

We get rid of parentheses

42v^2+49v+54v+63=0

We add all the numbers together, and all the variables

42v^2+103v+63=0

a = 42; b = 103; c = +63;
Δ = b2-4ac
Δ = 1032-4·42·63
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(103)-5}{2*42}=\frac{-108}{84}
=-1+2/7
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(103)+5}{2*42}=\frac{-98}{84}
=-1+1/6
$