0.024t^2-0.578t+2.309=0

Solution for 0.024t^2-0.578t+2.309=0 equation:

0.024t^2-0.578t+2.309=0

a = 0.024; b = -0.578; c = +2.309;
Δ = b2-4ac
Δ = -0.5782-4·0.024·2.309
Δ = 0.11242
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{-(-0.578)-\sqrt{0.11242}}{2*0.024}=\frac{0.578-\sqrt{0.11242}}{0.048}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.578)+\sqrt{0.11242}}{2*0.024}=\frac{0.578+\sqrt{0.11242}}{0.048}
$