0.038*0.25-1x+x^2=4x^2

Solution for 0.038*0.25-1x+x^2=4x^2 equation:

0.038*0.25-1x+x^2=4x^2

We move all terms to the left:

0.038*0.25-1x+x^2-(4x^2)=0

determiningTheFunctionDomain
x^2-4x^2-1x+0.038*0.25=0

We add all the numbers together, and all the variables

-3x^2-1x+0.0095=0

a = -3; b = -1; c = +0.0095;
Δ = b2-4ac
Δ = -12-4·(-3)·0.0095
Δ = 1.114
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)-\sqrt{1.114}}{2*-3}=\frac{1-\sqrt{1.114}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1.114}}{2*-3}=\frac{1+\sqrt{1.114}}{-6}
$