3t*t-12t+40=55

Solution for 3t*t-12t+40=55 equation:

3t*t-12t+40=55

We move all terms to the left:

3t*t-12t+40-(55)=0

We add all the numbers together, and all the variables

-12t+3t*t-15=0

Wy multiply elements

3t^2-12t-15=0

a = 3; b = -12; c = -15;
Δ = b2-4ac
Δ = -122-4·3·(-15)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-18}{2*3}=\frac{-6}{6}
=-1
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+18}{2*3}=\frac{30}{6}
=5
$