5t+2t^2=81

Solution for 5t+2t^2=81 equation:

5t+2t^2=81

We move all terms to the left:

5t+2t^2-(81)=0

a = 2; b = 5; c = -81;
Δ = b2-4ac
Δ = 52-4·2·(-81)
Δ = 673
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{673}}{2*2}=\frac{-5-\sqrt{673}}{4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{673}}{2*2}=\frac{-5+\sqrt{673}}{4}
$