49t^2-30t-80=0

Solution for 49t^2-30t-80=0 equation:

49t^2-30t-80=0

a = 49; b = -30; c = -80;
Δ = b2-4ac
Δ = -302-4·49·(-80)
Δ = 16580
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:

$\sqrt{\Delta}=\sqrt{16580}=\sqrt{4*4145}=\sqrt{4}*\sqrt{4145}=2\sqrt{4145}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{4145}}{2*49}=\frac{30-2\sqrt{4145}}{98}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{4145}}{2*49}=\frac{30+2\sqrt{4145}}{98}
$