-7n^2=53n+28

Solution for -7n^2=53n+28 equation:

-7n^2=53n+28

We move all terms to the left:

-7n^2-(53n+28)=0

We get rid of parentheses

-7n^2-53n-28=0

a = -7; b = -53; c = -28;
Δ = b2-4ac
Δ = -532-4·(-7)·(-28)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-45}{2*-7}=\frac{8}{-14}
=-4/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+45}{2*-7}=\frac{98}{-14}
=-7
$