5n^2+240=70n

Solution for 5n^2+240=70n equation:

5n^2+240=70n

We move all terms to the left:

5n^2+240-(70n)=0

a = 5; b = -70; c = +240;
Δ = b2-4ac
Δ = -702-4·5·240
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{-(-70)-10}{2*5}=\frac{60}{10}
=6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+10}{2*5}=\frac{80}{10}
=8
$