9.01t^2-20.60t+23.55=9.47t^2-21.46t+18.72

Solution for 9.01t^2-20.60t+23.55=9.47t^2-21.46t+18.72 equation:

9.01t^2-20.60t+23.55=9.47t^2-21.46t+18.72

We move all terms to the left:

9.01t^2-20.60t+23.55-(9.47t^2-21.46t+18.72)=0

We add all the numbers together, and all the variables

9.01t^2-20.6t-(9.47t^2-21.46t+18.72)+23.55=0

We get rid of parentheses

9.01t^2-9.47t^2-20.6t+21.46t-18.72+23.55=0

We add all the numbers together, and all the variables

-0.46t^2+0.86t+4.83=0

a = -0.46; b = 0.86; c = +4.83;
Δ = b2-4ac
Δ = 0.862-4·(-0.46)·4.83
Δ = 9.6268
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{-(0.86)-\sqrt{9.6268}}{2*-0.46}=\frac{-0.86-\sqrt{9.6268}}{-0.92}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.86)+\sqrt{9.6268}}{2*-0.46}=\frac{-0.86+\sqrt{9.6268}}{-0.92}
$