19=7+29t+26t^2

Solution for 19=7+29t+26t^2 equation:

19=7+29t+26t^2

We move all terms to the left:

19-(7+29t+26t^2)=0

We get rid of parentheses

-26t^2-29t-7+19=0

We add all the numbers together, and all the variables

-26t^2-29t+12=0

a = -26; b = -29; c = +12;
Δ = b2-4ac
Δ = -292-4·(-26)·12
Δ = 2089
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{-(-29)-\sqrt{2089}}{2*-26}=\frac{29-\sqrt{2089}}{-52}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{2089}}{2*-26}=\frac{29+\sqrt{2089}}{-52}
$