45n^2=80

Solution for 45n^2=80 equation:

45n^2=80

We move all terms to the left:

45n^2-(80)=0

a = 45; b = 0; c = -80;
Δ = b2-4ac
Δ = 02-4·45·(-80)
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-120}{2*45}=\frac{-120}{90}
=-1+1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+120}{2*45}=\frac{120}{90}
=1+1/3
$