t^2-59t+54-82t^2=0

Solution for t^2-59t+54-82t^2=0 equation:

t^2-59t+54-82t^2=0

We add all the numbers together, and all the variables

-81t^2-59t+54=0

a = -81; b = -59; c = +54;
Δ = b2-4ac
Δ = -592-4·(-81)·54
Δ = 20977
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{-(-59)-\sqrt{20977}}{2*-81}=\frac{59-\sqrt{20977}}{-162}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+\sqrt{20977}}{2*-81}=\frac{59+\sqrt{20977}}{-162}
$