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

Solution for -2(t+5)5t=6t+11 equation:

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

We move all terms to the left:

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

We multiply parentheses

-10t^2-50t-(6t+11)=0

We get rid of parentheses

-10t^2-50t-6t-11=0

We add all the numbers together, and all the variables

-10t^2-56t-11=0

a = -10; b = -56; c = -11;
Δ = b2-4ac
Δ = -562-4·(-10)·(-11)
Δ = 2696
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:

$\sqrt{\Delta}=\sqrt{2696}=\sqrt{4*674}=\sqrt{4}*\sqrt{674}=2\sqrt{674}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-2\sqrt{674}}{2*-10}=\frac{56-2\sqrt{674}}{-20}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+2\sqrt{674}}{2*-10}=\frac{56+2\sqrt{674}}{-20}
$