4(7n+6)(n+5)=0

Solution for 4(7n+6)(n+5)=0 equation:

4(7n+6)(n+5)=0

We multiply parentheses ..

4(+7n^2+35n+6n+30)=0

We multiply parentheses

28n^2+140n+24n+120=0

We add all the numbers together, and all the variables

28n^2+164n+120=0

a = 28; b = 164; c = +120;
Δ = b2-4ac
Δ = 1642-4·28·120
Δ = 13456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13456}=116$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(164)-116}{2*28}=\frac{-280}{56}
=-5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(164)+116}{2*28}=\frac{-48}{56}
=-6/7
$