t=7t^2-38t-77

Solution for t=7t^2-38t-77 equation:

t=7t^2-38t-77

We move all terms to the left:

t-(7t^2-38t-77)=0

We get rid of parentheses

-7t^2+t+38t+77=0

We add all the numbers together, and all the variables

-7t^2+39t+77=0

a = -7; b = 39; c = +77;
Δ = b2-4ac
Δ = 392-4·(-7)·77
Δ = 3677
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{-(39)-\sqrt{3677}}{2*-7}=\frac{-39-\sqrt{3677}}{-14}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+\sqrt{3677}}{2*-7}=\frac{-39+\sqrt{3677}}{-14}
$