7n^2-65n=-72

Solution for 7n^2-65n=-72 equation:

7n^2-65n=-72

We move all terms to the left:

7n^2-65n-(-72)=0

We add all the numbers together, and all the variables

7n^2-65n+72=0

a = 7; b = -65; c = +72;
Δ = b2-4ac
Δ = -652-4·7·72
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-47}{2*7}=\frac{18}{14}
=1+2/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+47}{2*7}=\frac{112}{14}
=8
$