t^2-5t=32

Solution for t^2-5t=32 equation:

t^2-5t=32

We move all terms to the left:

t^2-5t-(32)=0

a = 1; b = -5; c = -32;
Δ = b2-4ac
Δ = -52-4·1·(-32)
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{17}}{2*1}=\frac{5-3\sqrt{17}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{17}}{2*1}=\frac{5+3\sqrt{17}}{2}
$