13t=16(t-1/6)

Solution for 13t=16(t-1/6) equation:

13t=16(t-1/6)

We move all terms to the left:

13t-(16(t-1/6))=0

We add all the numbers together, and all the variables

13t-(16(+t-1/6))=0

We multiply all the terms by the denominator


13t*6))-(16(+t-1=0

We add all the numbers together, and all the variables

t+13t*6))-(16(-1=0

Wy multiply elements

78t^2+t-1=0

a = 78; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·78·(-1)
Δ = 313
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{313}}{2*78}=\frac{-1-\sqrt{313}}{156}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{313}}{2*78}=\frac{-1+\sqrt{313}}{156}
$