5(t-9)12,t=20

Solution for 5(t-9)12,t=20 equation:

5(t-9)12.t=20

We move all terms to the left:

5(t-9)12.t-(20)=0

We multiply parentheses

60t^2-540t-20=0

a = 60; b = -540; c = -20;
Δ = b2-4ac
Δ = -5402-4·60·(-20)
Δ = 296400
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:

$\sqrt{\Delta}=\sqrt{296400}=\sqrt{400*741}=\sqrt{400}*\sqrt{741}=20\sqrt{741}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-20\sqrt{741}}{2*60}=\frac{540-20\sqrt{741}}{120}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+20\sqrt{741}}{2*60}=\frac{540+20\sqrt{741}}{120}
$