5t^2-60t+45=0

Solution for 5t^2-60t+45=0 equation:

5t^2-60t+45=0

a = 5; b = -60; c = +45;
Δ = b2-4ac
Δ = -602-4·5·45
Δ = 2700
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:

$\sqrt{\Delta}=\sqrt{2700}=\sqrt{900*3}=\sqrt{900}*\sqrt{3}=30\sqrt{3}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-30\sqrt{3}}{2*5}=\frac{60-30\sqrt{3}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+30\sqrt{3}}{2*5}=\frac{60+30\sqrt{3}}{10}
$