49t^2-80t-23=0

Solution for 49t^2-80t-23=0 equation:

49t^2-80t-23=0

a = 49; b = -80; c = -23;
Δ = b2-4ac
Δ = -802-4·49·(-23)
Δ = 10908
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:

$\sqrt{\Delta}=\sqrt{10908}=\sqrt{36*303}=\sqrt{36}*\sqrt{303}=6\sqrt{303}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-6\sqrt{303}}{2*49}=\frac{80-6\sqrt{303}}{98}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+6\sqrt{303}}{2*49}=\frac{80+6\sqrt{303}}{98}
$