-4.095t^2+7.5t+31=0

Solution for -4.095t^2+7.5t+31=0 equation:

-4.095t^2+7.5t+31=0

a = -4.095; b = 7.5; c = +31;
Δ = b2-4ac
Δ = 7.52-4·(-4.095)·31
Δ = 564.03
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{-(7.5)-\sqrt{564.03}}{2*-4.095}=\frac{-7.5-\sqrt{564.03}}{-8.19}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7.5)+\sqrt{564.03}}{2*-4.095}=\frac{-7.5+\sqrt{564.03}}{-8.19}
$