7n^2+25=40n

Solution for 7n^2+25=40n equation:

7n^2+25=40n

We move all terms to the left:

7n^2+25-(40n)=0

a = 7; b = -40; c = +25;
Δ = b2-4ac
Δ = -402-4·7·25
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-30}{2*7}=\frac{10}{14}
=5/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+30}{2*7}=\frac{70}{14}
=5
$