17-3n(2n-5)=30-6n

Solution for 17-3n(2n-5)=30-6n equation:

17-3n(2n-5)=30-6n

We move all terms to the left:

17-3n(2n-5)-(30-6n)=0

We add all the numbers together, and all the variables

-3n(2n-5)-(-6n+30)+17=0

We multiply parentheses

-6n^2+15n-(-6n+30)+17=0

We get rid of parentheses

-6n^2+15n+6n-30+17=0

We add all the numbers together, and all the variables

-6n^2+21n-13=0

a = -6; b = 21; c = -13;
Δ = b2-4ac
Δ = 212-4·(-6)·(-13)
Δ = 129
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{-(21)-\sqrt{129}}{2*-6}=\frac{-21-\sqrt{129}}{-12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{129}}{2*-6}=\frac{-21+\sqrt{129}}{-12}
$