4t^2-40t-51=0

Solution for 4t^2-40t-51=0 equation:

4t^2-40t-51=0

a = 4; b = -40; c = -51;
Δ = b2-4ac
Δ = -402-4·4·(-51)
Δ = 2416
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:

$\sqrt{\Delta}=\sqrt{2416}=\sqrt{16*151}=\sqrt{16}*\sqrt{151}=4\sqrt{151}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{151}}{2*4}=\frac{40-4\sqrt{151}}{8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{151}}{2*4}=\frac{40+4\sqrt{151}}{8}
$