t^2-70t+612.5=0

Solution for t^2-70t+612.5=0 equation:

t^2-70t+612.5=0

a = 1; b = -70; c = +612.5;
Δ = b2-4ac
Δ = -702-4·1·612.5
Δ = 2450
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:

$\sqrt{\Delta}=\sqrt{2450}=\sqrt{1225*2}=\sqrt{1225}*\sqrt{2}=35\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-35\sqrt{2}}{2*1}=\frac{70-35\sqrt{2}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+35\sqrt{2}}{2*1}=\frac{70+35\sqrt{2}}{2}
$