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21(n+4)n-8n=3
We move all terms to the left:
21(n+4)n-8n-(3)=0
We add all the numbers together, and all the variables
-8n+21(n+4)n-3=0
We multiply parentheses
21n^2-8n+84n-3=0
We add all the numbers together, and all the variables
21n^2+76n-3=0
a = 21; b = 76; c = -3;
Δ = b2-4ac
Δ = 762-4·21·(-3)
Δ = 6028
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6028}=\sqrt{4*1507}=\sqrt{4}*\sqrt{1507}=2\sqrt{1507}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-2\sqrt{1507}}{2*21}=\frac{-76-2\sqrt{1507}}{42} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+2\sqrt{1507}}{2*21}=\frac{-76+2\sqrt{1507}}{42} $
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