t^2-9t=12

Solution for t^2-9t=12 equation:

t^2-9t=12

We move all terms to the left:

t^2-9t-(12)=0

a = 1; b = -9; c = -12;
Δ = b2-4ac
Δ = -92-4·1·(-12)
Δ = 129
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{-(-9)-\sqrt{129}}{2*1}=\frac{9-\sqrt{129}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{129}}{2*1}=\frac{9+\sqrt{129}}{2}
$