43-4t-5t^2=0

Solution for 43-4t-5t^2=0 equation:

43-4t-5t^2=0

a = -5; b = -4; c = +43;
Δ = b2-4ac
Δ = -42-4·(-5)·43
Δ = 876
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:

$\sqrt{\Delta}=\sqrt{876}=\sqrt{4*219}=\sqrt{4}*\sqrt{219}=2\sqrt{219}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{219}}{2*-5}=\frac{4-2\sqrt{219}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{219}}{2*-5}=\frac{4+2\sqrt{219}}{-10}
$