2t^2-39t+180=0

Solution for 2t^2-39t+180=0 equation:

2t^2-39t+180=0

a = 2; b = -39; c = +180;
Δ = b2-4ac
Δ = -392-4·2·180
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-9}{2*2}=\frac{30}{4}
=7+1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+9}{2*2}=\frac{48}{4}
=12
$