1-5n^2/4=-31

Solution for 1-5n^2/4=-31 equation:

1-5n^2/4=-31

We move all terms to the left:

1-5n^2/4-(-31)=0

We add all the numbers together, and all the variables

-5n^2/4+32=0

We multiply all the terms by the denominator


-5n^2+32*4=0

We add all the numbers together, and all the variables

-5n^2+128=0

a = -5; b = 0; c = +128;
Δ = b2-4ac
Δ = 02-4·(-5)·128
Δ = 2560
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2560}=\sqrt{256*10}=\sqrt{256}*\sqrt{10}=16\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{10}}{2*-5}=\frac{0-16\sqrt{10}}{-10}
=-\frac{16\sqrt{10}}{-10}
=-\frac{8\sqrt{10}}{-5}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{10}}{2*-5}=\frac{0+16\sqrt{10}}{-10}
=\frac{16\sqrt{10}}{-10}
=\frac{8\sqrt{10}}{-5}
$