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(7n-7)(n-7)=51
We move all terms to the left:
(7n-7)(n-7)-(51)=0
We multiply parentheses ..
(+7n^2-49n-7n+49)-51=0
We get rid of parentheses
7n^2-49n-7n+49-51=0
We add all the numbers together, and all the variables
7n^2-56n-2=0
a = 7; b = -56; c = -2;
Δ = b2-4ac
Δ = -562-4·7·(-2)
Δ = 3192
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3192}=\sqrt{4*798}=\sqrt{4}*\sqrt{798}=2\sqrt{798}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-2\sqrt{798}}{2*7}=\frac{56-2\sqrt{798}}{14} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+2\sqrt{798}}{2*7}=\frac{56+2\sqrt{798}}{14} $
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