-4=-4t^2-5t

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

-4=-4t^2-5t

We move all terms to the left:

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

We get rid of parentheses

4t^2+5t-4=0

a = 4; b = 5; c = -4;
Δ = b2-4ac
Δ = 52-4·4·(-4)
Δ = 89
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{-(5)-\sqrt{89}}{2*4}=\frac{-5-\sqrt{89}}{8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{89}}{2*4}=\frac{-5+\sqrt{89}}{8}
$