7n^2=27n+40

Solution for 7n^2=27n+40 equation:

7n^2=27n+40

We move all terms to the left:

7n^2-(27n+40)=0

We get rid of parentheses

7n^2-27n-40=0

a = 7; b = -27; c = -40;
Δ = b2-4ac
Δ = -272-4·7·(-40)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-43}{2*7}=\frac{-16}{14}
=-1+1/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+43}{2*7}=\frac{70}{14}
=5
$