(5v+3)(7v-8)=0

Solution for (5v+3)(7v-8)=0 equation:

(5v+3)(7v-8)=0

We multiply parentheses ..

(+35v^2-40v+21v-24)=0

We get rid of parentheses

35v^2-40v+21v-24=0

We add all the numbers together, and all the variables

35v^2-19v-24=0

a = 35; b = -19; c = -24;
Δ = b2-4ac
Δ = -192-4·35·(-24)
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-61}{2*35}=\frac{-42}{70}
=-3/5
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+61}{2*35}=\frac{80}{70}
=1+1/7
$