4t^2-30t-1=0

Solution for 4t^2-30t-1=0 equation:

4t^2-30t-1=0

a = 4; b = -30; c = -1;
Δ = b2-4ac
Δ = -302-4·4·(-1)
Δ = 916
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:

$\sqrt{\Delta}=\sqrt{916}=\sqrt{4*229}=\sqrt{4}*\sqrt{229}=2\sqrt{229}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{229}}{2*4}=\frac{30-2\sqrt{229}}{8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{229}}{2*4}=\frac{30+2\sqrt{229}}{8}
$