7(7n+5)(n+1)=0

Solution for 7(7n+5)(n+1)=0 equation:

7(7n+5)(n+1)=0

We multiply parentheses ..

7(+7n^2+7n+5n+5)=0

We multiply parentheses

49n^2+49n+35n+35=0

We add all the numbers together, and all the variables

49n^2+84n+35=0

a = 49; b = 84; c = +35;
Δ = b2-4ac
Δ = 842-4·49·35
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-14}{2*49}=\frac{-98}{98}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+14}{2*49}=\frac{-70}{98}
=-5/7
$