4.75t^2+2t-80=0

Solution for 4.75t^2+2t-80=0 equation:

4.75t^2+2t-80=0

a = 4.75; b = 2; c = -80;
Δ = b2-4ac
Δ = 22-4·4.75·(-80)
Δ = 1524
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:

$\sqrt{\Delta}=\sqrt{1524}=\sqrt{4*381}=\sqrt{4}*\sqrt{381}=2\sqrt{381}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{381}}{2*4.75}=\frac{-2-2\sqrt{381}}{9.5}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{381}}{2*4.75}=\frac{-2+2\sqrt{381}}{9.5}
$