t^2-60t+450=900

Solution for t^2-60t+450=900 equation:

t^2-60t+450=900

We move all terms to the left:

t^2-60t+450-(900)=0

We add all the numbers together, and all the variables

t^2-60t-450=0

a = 1; b = -60; c = -450;
Δ = b2-4ac
Δ = -602-4·1·(-450)
Δ = 5400
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:

$\sqrt{\Delta}=\sqrt{5400}=\sqrt{900*6}=\sqrt{900}*\sqrt{6}=30\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-30\sqrt{6}}{2*1}=\frac{60-30\sqrt{6}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+30\sqrt{6}}{2*1}=\frac{60+30\sqrt{6}}{2}
$