t^2-34t-4=0

Solution for t^2-34t-4=0 equation:

t^2-34t-4=0

a = 1; b = -34; c = -4;
Δ = b2-4ac
Δ = -342-4·1·(-4)
Δ = 1172
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:

$\sqrt{\Delta}=\sqrt{1172}=\sqrt{4*293}=\sqrt{4}*\sqrt{293}=2\sqrt{293}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{293}}{2*1}=\frac{34-2\sqrt{293}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{293}}{2*1}=\frac{34+2\sqrt{293}}{2}
$