4-5n^2=-88

Solution for 4-5n^2=-88 equation:

4-5n^2=-88

We move all terms to the left:

4-5n^2-(-88)=0

We add all the numbers together, and all the variables

-5n^2+92=0

a = -5; b = 0; c = +92;
Δ = b2-4ac
Δ = 02-4·(-5)·92
Δ = 1840
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:

$\sqrt{\Delta}=\sqrt{1840}=\sqrt{16*115}=\sqrt{16}*\sqrt{115}=4\sqrt{115}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{115}}{2*-5}=\frac{0-4\sqrt{115}}{-10}
=-\frac{4\sqrt{115}}{-10}
=-\frac{2\sqrt{115}}{-5}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{115}}{2*-5}=\frac{0+4\sqrt{115}}{-10}
=\frac{4\sqrt{115}}{-10}
=\frac{2\sqrt{115}}{-5}
$