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7n^2-64n+64=0
a = 7; b = -64; c = +64;
Δ = b2-4ac
Δ = -642-4·7·64
Δ = 2304
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{2304}=48$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-48}{2*7}=\frac{16}{14} =1+1/7 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+48}{2*7}=\frac{112}{14} =8 $
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