X=10t+4t^2

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

X=10X+4X^2

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-4X^2-9X=0

a = -4; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-4)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-4}=\frac{0}{-8}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-4}=\frac{18}{-8}
=-2+1/4
$