0.056t^2-0.93t+15.2=52

Solution for 0.056t^2-0.93t+15.2=52 equation:

0.056t^2-0.93t+15.2=52

We move all terms to the left:

0.056t^2-0.93t+15.2-(52)=0

We add all the numbers together, and all the variables

0.056t^2-0.93t-36.8=0

a = 0.056; b = -0.93; c = -36.8;
Δ = b2-4ac
Δ = -0.932-4·0.056·(-36.8)
Δ = 9.1081
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{-(-0.93)-\sqrt{9.1081}}{2*0.056}=\frac{0.93-\sqrt{9.1081}}{0.112}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.93)+\sqrt{9.1081}}{2*0.056}=\frac{0.93+\sqrt{9.1081}}{0.112}
$