4t^2-2t-75=0

Solution for 4t^2-2t-75=0 equation:

4t^2-2t-75=0

a = 4; b = -2; c = -75;
Δ = b2-4ac
Δ = -22-4·4·(-75)
Δ = 1204
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:

$\sqrt{\Delta}=\sqrt{1204}=\sqrt{4*301}=\sqrt{4}*\sqrt{301}=2\sqrt{301}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{301}}{2*4}=\frac{2-2\sqrt{301}}{8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{301}}{2*4}=\frac{2+2\sqrt{301}}{8}
$