6t^2-13t=5

Solution for 6t^2-13t=5 equation:

6t^2-13t=5

We move all terms to the left:

6t^2-13t-(5)=0

a = 6; b = -13; c = -5;
Δ = b2-4ac
Δ = -132-4·6·(-5)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-17}{2*6}=\frac{-4}{12}
=-1/3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+17}{2*6}=\frac{30}{12}
=2+1/2
$