t^2-10t=-17

Solution for t^2-10t=-17 equation:

t^2-10t=-17

We move all terms to the left:

t^2-10t-(-17)=0

We add all the numbers together, and all the variables

t^2-10t+17=0

a = 1; b = -10; c = +17;
Δ = b2-4ac
Δ = -102-4·1·17
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{2}}{2*1}=\frac{10-4\sqrt{2}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{2}}{2*1}=\frac{10+4\sqrt{2}}{2}
$