t^2-5t=31.25

Solution for t^2-5t=31.25 equation:

t^2-5t=31.25

We move all terms to the left:

t^2-5t-(31.25)=0

We add all the numbers together, and all the variables

t^2-5t-31.25=0

a = 1; b = -5; c = -31.25;
Δ = b2-4ac
Δ = -52-4·1·(-31.25)
Δ = 150
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:

$\sqrt{\Delta}=\sqrt{150}=\sqrt{25*6}=\sqrt{25}*\sqrt{6}=5\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{6}}{2*1}=\frac{5-5\sqrt{6}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{6}}{2*1}=\frac{5+5\sqrt{6}}{2}
$