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7n^2=9-10n
We move all terms to the left:
7n^2-(9-10n)=0
We add all the numbers together, and all the variables
7n^2-(-10n+9)=0
We get rid of parentheses
7n^2+10n-9=0
a = 7; b = 10; c = -9;
Δ = b2-4ac
Δ = 102-4·7·(-9)
Δ = 352
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{22}}{2*7}=\frac{-10-4\sqrt{22}}{14} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{22}}{2*7}=\frac{-10+4\sqrt{22}}{14} $
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