2=4t^2+10t+2

Solution for 2=4t^2+10t+2 equation:

2=4t^2+10t+2

We move all terms to the left:

2-(4t^2+10t+2)=0

We get rid of parentheses

-4t^2-10t-2+2=0

We add all the numbers together, and all the variables

-4t^2-10t=0

a = -4; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-4)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-4}=\frac{0}{-8}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-4}=\frac{20}{-8}
=-2+1/2
$