4n^2-23=-5n

Solution for 4n^2-23=-5n equation:

4n^2-23=-5n

We move all terms to the left:

4n^2-23-(-5n)=0

We get rid of parentheses

4n^2+5n-23=0

a = 4; b = 5; c = -23;
Δ = b2-4ac
Δ = 52-4·4·(-23)
Δ = 393
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{393}}{2*4}=\frac{-5-\sqrt{393}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{393}}{2*4}=\frac{-5+\sqrt{393}}{8}
$