-5n(3n-5)-4=-1-4n

Solution for -5n(3n-5)-4=-1-4n equation:

-5n(3n-5)-4=-1-4n

We move all terms to the left:

-5n(3n-5)-4-(-1-4n)=0

We add all the numbers together, and all the variables

-5n(3n-5)-(-4n-1)-4=0

We multiply parentheses

-15n^2+25n-(-4n-1)-4=0

We get rid of parentheses

-15n^2+25n+4n+1-4=0

We add all the numbers together, and all the variables

-15n^2+29n-3=0

a = -15; b = 29; c = -3;
Δ = b2-4ac
Δ = 292-4·(-15)·(-3)
Δ = 661
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{-(29)-\sqrt{661}}{2*-15}=\frac{-29-\sqrt{661}}{-30}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+\sqrt{661}}{2*-15}=\frac{-29+\sqrt{661}}{-30}
$