Solve for t
t = -\frac{\sqrt{249}}{3} \approx -5.259911279
t = \frac{\sqrt{249}}{3} \approx 5.259911279
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33t^{2}+1826t-75779=0
Substitute t for t^{2}.
t=\frac{-1826±\sqrt{1826^{2}-4\times 33\left(-75779\right)}}{2\times 33}
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 33 for a, 1826 for b, and -75779 for c in the quadratic formula.
t=\frac{-1826±3652}{66}
Do the calculations.
t=\frac{83}{3} t=-83
Solve the equation t=\frac{-1826±3652}{66} when ± is plus and when ± is minus.
t=\frac{\sqrt{249}}{3} t=-\frac{\sqrt{249}}{3}
Since t=t^{2}, the solutions are obtained by evaluating t=±\sqrt{t} for positive t.
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