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9n^2-45n-162=21n
We move all terms to the left:
9n^2-45n-162-(21n)=0
We add all the numbers together, and all the variables
9n^2-66n-162=0
a = 9; b = -66; c = -162;
Δ = b2-4ac
Δ = -662-4·9·(-162)
Δ = 10188
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10188}=\sqrt{36*283}=\sqrt{36}*\sqrt{283}=6\sqrt{283}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-6\sqrt{283}}{2*9}=\frac{66-6\sqrt{283}}{18} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+6\sqrt{283}}{2*9}=\frac{66+6\sqrt{283}}{18} $
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