(0.02-0.3x+x^2)/(0.01+0.4x+4x^2)=0

Solution for (0.02-0.3x+x^2)/(0.01+0.4x+4x^2)=0 equation:

(0.02-0.3x+x^2)/(0.01+0.4x+4x^2)=0


Domain of the equation: (0.01+0.4x+4x^2)!=0

We move all terms containing x to the left, all other terms to the right

4x^2+0.4x!=-0.01

x∈R


We multiply all the terms by the denominator


(0.02-0.3x+x^2)=0

We get rid of parentheses

x^2-0.3x+0.02=0

a = 1; b = -0.3; c = +0.02;
Δ = b2-4ac
Δ = -0.32-4·1·0.02
Δ = 0.01
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{-(-0.3)-\sqrt{0.01}}{2*1}=\frac{0.3-\sqrt{0.01}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.3)+\sqrt{0.01}}{2*1}=\frac{0.3+\sqrt{0.01}}{2}
$