88=7n^2+45n

Solution for 88=7n^2+45n equation:

88=7n^2+45n

We move all terms to the left:

88-(7n^2+45n)=0

We get rid of parentheses

-7n^2-45n+88=0

a = -7; b = -45; c = +88;
Δ = b2-4ac
Δ = -452-4·(-7)·88
Δ = 4489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4489}=67$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-67}{2*-7}=\frac{-22}{-14}
=1+4/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+67}{2*-7}=\frac{112}{-14}
=-8
$