(6t-7t2)+11(7t+5)=t

Solution for (6t-7t2)+11(7t+5)=t equation:

(6t-7t^2)+11(7t+5)=t

We move all terms to the left:

(6t-7t^2)+11(7t+5)-(t)=0

We add all the numbers together, and all the variables

(6t-7t^2)-1t+11(7t+5)=0

We multiply parentheses

(6t-7t^2)-1t+77t+55=0

We get rid of parentheses

-7t^2+6t-1t+77t+55=0

We add all the numbers together, and all the variables

-7t^2+82t+55=0

a = -7; b = 82; c = +55;
Δ = b2-4ac
Δ = 822-4·(-7)·55
Δ = 8264
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:

$\sqrt{\Delta}=\sqrt{8264}=\sqrt{4*2066}=\sqrt{4}*\sqrt{2066}=2\sqrt{2066}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(82)-2\sqrt{2066}}{2*-7}=\frac{-82-2\sqrt{2066}}{-14}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(82)+2\sqrt{2066}}{2*-7}=\frac{-82+2\sqrt{2066}}{-14}
$