-n(4n+5)-37n=(-9n-3)(n+4)+14

Solution for -n(4n+5)-37n=(-9n-3)(n+4)+14 equation:

-n(4n+5)-37n=(-9n-3)(n+4)+14

We move all terms to the left:

-n(4n+5)-37n-((-9n-3)(n+4)+14)=0

We add all the numbers together, and all the variables

-37n-n(4n+5)-((-9n-3)(n+4)+14)=0

We multiply parentheses

-4n^2-37n-5n-((-9n-3)(n+4)+14)=0

We multiply parentheses ..

-4n^2-((-9n^2-36n-3n-12)+14)-37n-5n=0


We calculate terms in parentheses: -((-9n^2-36n-3n-12)+14), so:

(-9n^2-36n-3n-12)+14

We get rid of parentheses

-9n^2-36n-3n-12+14

We add all the numbers together, and all the variables

-9n^2-39n+2

Back to the equation:

-(-9n^2-39n+2)


We add all the numbers together, and all the variables

-4n^2-(-9n^2-39n+2)-42n=0

We get rid of parentheses

-4n^2+9n^2+39n-42n-2=0

We add all the numbers together, and all the variables

5n^2-3n-2=0

a = 5; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·5·(-2)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-7}{2*5}=\frac{-4}{10}
=-2/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+7}{2*5}=\frac{10}{10}
=1
$