3=-5t^2+14t+3

Solution for 3=-5t^2+14t+3 equation:

3=-5t^2+14t+3

We move all terms to the left:

3-(-5t^2+14t+3)=0

We get rid of parentheses

5t^2-14t-3+3=0

We add all the numbers together, and all the variables

5t^2-14t=0

a = 5; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·5·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*5}=\frac{0}{10}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*5}=\frac{28}{10}
=2+4/5
$