6=5t^2+10t+1

Solution for 6=5t^2+10t+1 equation:

6=5t^2+10t+1

We move all terms to the left:

6-(5t^2+10t+1)=0

We get rid of parentheses

-5t^2-10t-1+6=0

We add all the numbers together, and all the variables

-5t^2-10t+5=0

a = -5; b = -10; c = +5;
Δ = b2-4ac
Δ = -102-4·(-5)·5
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{2}}{2*-5}=\frac{10-10\sqrt{2}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{2}}{2*-5}=\frac{10+10\sqrt{2}}{-10}
$