2t^2-50t-315=0

Solution for 2t^2-50t-315=0 equation:

2t^2-50t-315=0

a = 2; b = -50; c = -315;
Δ = b2-4ac
Δ = -502-4·2·(-315)
Δ = 5020
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:

$\sqrt{\Delta}=\sqrt{5020}=\sqrt{4*1255}=\sqrt{4}*\sqrt{1255}=2\sqrt{1255}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{1255}}{2*2}=\frac{50-2\sqrt{1255}}{4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{1255}}{2*2}=\frac{50+2\sqrt{1255}}{4}
$