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If -nx2 + tx + c = 0, what is x equal to?

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konrad509
[tex]f(x)=-nx^2+tx+c=0\\\\ \Delta=t^2-4\cdot(-n)\cdot c=t^2+4cn\\\\ 1.\\ \Delta<0 \Rightarrow x\in\emptyset\\\\ 2.\\ \Delta=0\\ x=\frac{-t}{2\cdot(-n)}=\frac{t}{2n}\\\\ 3.\\ \Delta>0\\ \sqrt{\Delta}=\sqrt{t^2+4cn}\\ x_1=\frac{-t-\sqrt{t^2+4cn}}{2\cdot(-n)}=\frac{t+\sqrt{t^2+4cn}}{2n}\\ x_2=\frac{-t+\sqrt{t^2+4cn}}{2\cdot(-n)}=\frac{t-\sqrt{t^2+4cn}}{2n}\\[/tex]
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