t^2-9t-21=-6

Solution for t^2-9t-21=-6 equation:

t^2-9t-21=-6

We move all terms to the left:

t^2-9t-21-(-6)=0

We add all the numbers together, and all the variables

t^2-9t-15=0

a = 1; b = -9; c = -15;
Δ = b2-4ac
Δ = -92-4·1·(-15)
Δ = 141
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{141}}{2*1}=\frac{9-\sqrt{141}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{141}}{2*1}=\frac{9+\sqrt{141}}{2}
$