6t+t^2=66

Solution for 6t+t^2=66 equation:

6t+t^2=66

We move all terms to the left:

6t+t^2-(66)=0

a = 1; b = 6; c = -66;
Δ = b2-4ac
Δ = 62-4·1·(-66)
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-10\sqrt{3}}{2*1}=\frac{-6-10\sqrt{3}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+10\sqrt{3}}{2*1}=\frac{-6+10\sqrt{3}}{2}
$