5n^2+175=60n

Solution for 5n^2+175=60n equation:

5n^2+175=60n

We move all terms to the left:

5n^2+175-(60n)=0

a = 5; b = -60; c = +175;
Δ = b2-4ac
Δ = -602-4·5·175
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-10}{2*5}=\frac{50}{10}
=5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+10}{2*5}=\frac{70}{10}
=7
$