5n2+23=120-17

Solution for 5n2+23=120-17 equation:

5n^2+23=120-17

We move all terms to the left:

5n^2+23-(120-17)=0

We add all the numbers together, and all the variables

5n^2+23-103=0

We add all the numbers together, and all the variables

5n^2-80=0

a = 5; b = 0; c = -80;
Δ = b2-4ac
Δ = 02-4·5·(-80)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40}{2*5}=\frac{-40}{10}
=-4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40}{2*5}=\frac{40}{10}
=4
$