7n^2=-7n+84

Solution for 7n^2=-7n+84 equation:

7n^2=-7n+84

We move all terms to the left:

7n^2-(-7n+84)=0

We get rid of parentheses

7n^2+7n-84=0

a = 7; b = 7; c = -84;
Δ = b2-4ac
Δ = 72-4·7·(-84)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-49}{2*7}=\frac{-56}{14}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+49}{2*7}=\frac{42}{14}
=3
$