6t(2t-3)=36-6t

Solution for 6t(2t-3)=36-6t equation:

6t(2t-3)=36-6t

We move all terms to the left:

6t(2t-3)-(36-6t)=0

We add all the numbers together, and all the variables

6t(2t-3)-(-6t+36)=0

We multiply parentheses

12t^2-18t-(-6t+36)=0

We get rid of parentheses

12t^2-18t+6t-36=0

We add all the numbers together, and all the variables

12t^2-12t-36=0

a = 12; b = -12; c = -36;
Δ = b2-4ac
Δ = -122-4·12·(-36)
Δ = 1872
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:

$\sqrt{\Delta}=\sqrt{1872}=\sqrt{144*13}=\sqrt{144}*\sqrt{13}=12\sqrt{13}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{13}}{2*12}=\frac{12-12\sqrt{13}}{24}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{13}}{2*12}=\frac{12+12\sqrt{13}}{24}
$