10=-2.7t^2+50t+6.5

Solution for 10=-2.7t^2+50t+6.5 equation:

10=-2.7t^2+50t+6.5

We move all terms to the left:

10-(-2.7t^2+50t+6.5)=0

We get rid of parentheses

2.7t^2-50t-6.5+10=0

We add all the numbers together, and all the variables

2.7t^2-50t+3.5=0

a = 2.7; b = -50; c = +3.5;
Δ = b2-4ac
Δ = -502-4·2.7·3.5
Δ = 2462.2
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-\sqrt{2462.2}}{2*2.7}=\frac{50-\sqrt{2462.2}}{5.4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+\sqrt{2462.2}}{2*2.7}=\frac{50+\sqrt{2462.2}}{5.4}
$