t^2-45t-45=0

Solution for t^2-45t-45=0 equation:

t^2-45t-45=0

a = 1; b = -45; c = -45;
Δ = b2-4ac
Δ = -452-4·1·(-45)
Δ = 2205
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:

$\sqrt{\Delta}=\sqrt{2205}=\sqrt{441*5}=\sqrt{441}*\sqrt{5}=21\sqrt{5}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-21\sqrt{5}}{2*1}=\frac{45-21\sqrt{5}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+21\sqrt{5}}{2*1}=\frac{45+21\sqrt{5}}{2}
$