10T=-5t^2+15t+1

Solution for 10T=-5t^2+15t+1 equation:

10=-5T^2+15T+1

We move all terms to the left:

10-(-5T^2+15T+1)=0

We get rid of parentheses

5T^2-15T-1+10=0

We add all the numbers together, and all the variables

5T^2-15T+9=0

a = 5; b = -15; c = +9;
Δ = b2-4ac
Δ = -152-4·5·9
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{5}}{2*5}=\frac{15-3\sqrt{5}}{10}
$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{5}}{2*5}=\frac{15+3\sqrt{5}}{10}
$