0.024t^2-0.566t+2.301=0

Solution for 0.024t^2-0.566t+2.301=0 equation:

0.024t^2-0.566t+2.301=0

a = 0.024; b = -0.566; c = +2.301;
Δ = b2-4ac
Δ = -0.5662-4·0.024·2.301
Δ = 0.09946
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{-(-0.566)-\sqrt{0.09946}}{2*0.024}=\frac{0.566-\sqrt{0.09946}}{0.048}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.566)+\sqrt{0.09946}}{2*0.024}=\frac{0.566+\sqrt{0.09946}}{0.048}
$