t^2-6t^2+9t+3=0

Solution for t^2-6t^2+9t+3=0 equation:

t^2-6t^2+9t+3=0

We add all the numbers together, and all the variables

-5t^2+9t+3=0

a = -5; b = 9; c = +3;
Δ = b2-4ac
Δ = 92-4·(-5)·3
Δ = 141
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{-(9)-\sqrt{141}}{2*-5}=\frac{-9-\sqrt{141}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{141}}{2*-5}=\frac{-9+\sqrt{141}}{-10}
$