5.25t^2+2t-80=0

Solution for 5.25t^2+2t-80=0 equation:

5.25t^2+2t-80=0

a = 5.25; b = 2; c = -80;
Δ = b2-4ac
Δ = 22-4·5.25·(-80)
Δ = 1684
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:

$\sqrt{\Delta}=\sqrt{1684}=\sqrt{4*421}=\sqrt{4}*\sqrt{421}=2\sqrt{421}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{421}}{2*5.25}=\frac{-2-2\sqrt{421}}{10.5}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{421}}{2*5.25}=\frac{-2+2\sqrt{421}}{10.5}
$