18-7(2n-3)n=8

Solution for 18-7(2n-3)n=8 equation:

18-7(2n-3)n=8

We move all terms to the left:

18-7(2n-3)n-(8)=0

We add all the numbers together, and all the variables

-7(2n-3)n+10=0

We multiply parentheses

-14n^2+21n+10=0

a = -14; b = 21; c = +10;
Δ = b2-4ac
Δ = 212-4·(-14)·10
Δ = 1001
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{1001}}{2*-14}=\frac{-21-\sqrt{1001}}{-28}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{1001}}{2*-14}=\frac{-21+\sqrt{1001}}{-28}
$