4t^2-24t-37=0

Solution for 4t^2-24t-37=0 equation:

4t^2-24t-37=0

a = 4; b = -24; c = -37;
Δ = b2-4ac
Δ = -242-4·4·(-37)
Δ = 1168
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:

$\sqrt{\Delta}=\sqrt{1168}=\sqrt{16*73}=\sqrt{16}*\sqrt{73}=4\sqrt{73}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{73}}{2*4}=\frac{24-4\sqrt{73}}{8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{73}}{2*4}=\frac{24+4\sqrt{73}}{8}
$