6t2-55t=-9

Solution for 6t2-55t=-9 equation:

6t^2-55t=-9

We move all terms to the left:

6t^2-55t-(-9)=0

We add all the numbers together, and all the variables

6t^2-55t+9=0

a = 6; b = -55; c = +9;
Δ = b2-4ac
Δ = -552-4·6·9
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-53}{2*6}=\frac{2}{12}
=1/6
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+53}{2*6}=\frac{108}{12}
=9
$