t=-2t^2+36t-10

Solution for t=-2t^2+36t-10 equation:

t=-2t^2+36t-10

We move all terms to the left:

t-(-2t^2+36t-10)=0

We get rid of parentheses

2t^2-36t+t+10=0

We add all the numbers together, and all the variables

2t^2-35t+10=0

a = 2; b = -35; c = +10;
Δ = b2-4ac
Δ = -352-4·2·10
Δ = 1145
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{-(-35)-\sqrt{1145}}{2*2}=\frac{35-\sqrt{1145}}{4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{1145}}{2*2}=\frac{35+\sqrt{1145}}{4}
$