53t^2-72t+24=0

Solution for 53t^2-72t+24=0 equation:

53t^2-72t+24=0

a = 53; b = -72; c = +24;
Δ = b2-4ac
Δ = -722-4·53·24
Δ = 96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{6}}{2*53}=\frac{72-4\sqrt{6}}{106}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{6}}{2*53}=\frac{72+4\sqrt{6}}{106}
$