t^2-22t=-45

Solution for t^2-22t=-45 equation:

t^2-22t=-45

We move all terms to the left:

t^2-22t-(-45)=0

We add all the numbers together, and all the variables

t^2-22t+45=0

a = 1; b = -22; c = +45;
Δ = b2-4ac
Δ = -222-4·1·45
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-4\sqrt{19}}{2*1}=\frac{22-4\sqrt{19}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+4\sqrt{19}}{2*1}=\frac{22+4\sqrt{19}}{2}
$