4(5v+6)(v-2)=0

Solution for 4(5v+6)(v-2)=0 equation:

4(5v+6)(v-2)=0

We multiply parentheses ..

4(+5v^2-10v+6v-12)=0

We multiply parentheses

20v^2-40v+24v-48=0

We add all the numbers together, and all the variables

20v^2-16v-48=0

a = 20; b = -16; c = -48;
Δ = b2-4ac
Δ = -162-4·20·(-48)
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-64}{2*20}=\frac{-48}{40}
=-1+1/5
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+64}{2*20}=\frac{80}{40}
=2
$