-5.2t^2+72.3t+45=0

Solution for -5.2t^2+72.3t+45=0 equation:

-5.2t^2+72.3t+45=0

a = -5.2; b = 72.3; c = +45;
Δ = b2-4ac
Δ = 72.32-4·(-5.2)·45
Δ = 6163.29
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{-(72.3)-\sqrt{6163.29}}{2*-5.2}=\frac{-72.3-\sqrt{6163.29}}{-10.4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72.3)+\sqrt{6163.29}}{2*-5.2}=\frac{-72.3+\sqrt{6163.29}}{-10.4}
$