X=1.5+2.6t-3.8t^2

Solution for X=1.5+2.6t-3.8t^2 equation:

X=1.5+2.6X-3.8X^2

We move all terms to the left:

X-(1.5+2.6X-3.8X^2)=0

We get rid of parentheses

3.8X^2-2.6X+X-1.5=0

We add all the numbers together, and all the variables

3.8X^2-1.6X-1.5=0

a = 3.8; b = -1.6; c = -1.5;
Δ = b2-4ac
Δ = -1.62-4·3.8·(-1.5)
Δ = 25.36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1.6)-\sqrt{25.36}}{2*3.8}=\frac{1.6-\sqrt{25.36}}{7.6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.6)+\sqrt{25.36}}{2*3.8}=\frac{1.6+\sqrt{25.36}}{7.6}
$