(3n+8)(7n+7)=0

Solution for (3n+8)(7n+7)=0 equation:

(3n+8)(7n+7)=0

We multiply parentheses ..

(+21n^2+21n+56n+56)=0

We get rid of parentheses

21n^2+21n+56n+56=0

We add all the numbers together, and all the variables

21n^2+77n+56=0

a = 21; b = 77; c = +56;
Δ = b2-4ac
Δ = 772-4·21·56
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(77)-35}{2*21}=\frac{-112}{42}
=-2+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(77)+35}{2*21}=\frac{-42}{42}
=-1
$