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24n*12n=343n
We move all terms to the left:
24n*12n-(343n)=0
We add all the numbers together, and all the variables
-343n+24n*12n=0
Wy multiply elements
288n^2-343n=0
a = 288; b = -343; c = 0;
Δ = b2-4ac
Δ = -3432-4·288·0
Δ = 117649
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{117649}=343$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-343)-343}{2*288}=\frac{0}{576} =0 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-343)+343}{2*288}=\frac{686}{576} =1+55/288 $
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