0=-5t^2+6t+3

Solution for 0=-5t^2+6t+3 equation:

0=-5t^2+6t+3

We move all terms to the left:

0-(-5t^2+6t+3)=0

We add all the numbers together, and all the variables

-(-5t^2+6t+3)=0

We get rid of parentheses

5t^2-6t-3=0

a = 5; b = -6; c = -3;
Δ = b2-4ac
Δ = -62-4·5·(-3)
Δ = 96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{6}}{2*5}=\frac{6-4\sqrt{6}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{6}}{2*5}=\frac{6+4\sqrt{6}}{10}
$