-4n(n-5)+3n=10-3n

Solution for -4n(n-5)+3n=10-3n equation:

-4n(n-5)+3n=10-3n

We move all terms to the left:

-4n(n-5)+3n-(10-3n)=0

We add all the numbers together, and all the variables

-4n(n-5)+3n-(-3n+10)=0

We add all the numbers together, and all the variables

3n-4n(n-5)-(-3n+10)=0

We multiply parentheses

-4n^2+3n+20n-(-3n+10)=0

We get rid of parentheses

-4n^2+3n+20n+3n-10=0

We add all the numbers together, and all the variables

-4n^2+26n-10=0

a = -4; b = 26; c = -10;
Δ = b2-4ac
Δ = 262-4·(-4)·(-10)
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{129}}{2*-4}=\frac{-26-2\sqrt{129}}{-8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{129}}{2*-4}=\frac{-26+2\sqrt{129}}{-8}
$