(0.5)=60t-75t^2

Solution for (0.5)=60t-75t^2 equation:

(0.5)=60t-75t^2

We move all terms to the left:

(0.5)-(60t-75t^2)=0

We add all the numbers together, and all the variables

-(60t-75t^2)+0.5=0

We get rid of parentheses

75t^2-60t+0.5=0

a = 75; b = -60; c = +0.5;
Δ = b2-4ac
Δ = -602-4·75·0.5
Δ = 3450
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:

$\sqrt{\Delta}=\sqrt{3450}=\sqrt{25*138}=\sqrt{25}*\sqrt{138}=5\sqrt{138}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-5\sqrt{138}}{2*75}=\frac{60-5\sqrt{138}}{150}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+5\sqrt{138}}{2*75}=\frac{60+5\sqrt{138}}{150}
$