-5t^2+9t+2=4

Solution for -5t^2+9t+2=4 equation:

-5t^2+9t+2=4

We move all terms to the left:

-5t^2+9t+2-(4)=0

We add all the numbers together, and all the variables

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

a = -5; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·(-5)·(-2)
Δ = 41
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{41}}{2*-5}=\frac{-9-\sqrt{41}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{41}}{2*-5}=\frac{-9+\sqrt{41}}{-10}
$