-5n(1+7n)=-8

Solution for -5n(1+7n)=-8 equation:

-5n(1+7n)=-8

We move all terms to the left:

-5n(1+7n)-(-8)=0

We add all the numbers together, and all the variables

-5n(7n+1)-(-8)=0

We add all the numbers together, and all the variables

-5n(7n+1)+8=0

We multiply parentheses

-35n^2-5n+8=0

a = -35; b = -5; c = +8;
Δ = b2-4ac
Δ = -52-4·(-35)·8
Δ = 1145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{1145}}{2*-35}=\frac{5-\sqrt{1145}}{-70}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{1145}}{2*-35}=\frac{5+\sqrt{1145}}{-70}
$