(0.16+x^2)/(0.225-x^2)=4.0

Solution for (0.16+x^2)/(0.225-x^2)=4.0 equation:

(0.16+x^2)/(0.225-x^2)=4.0

We move all terms to the left:

(0.16+x^2)/(0.225-x^2)-(4.0)=0


Domain of the equation: (0.225-x^2)!=0

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

-x^2!=-0.225

x^2!=-0.225/-

x^2!=√0.225/

x!=0.47434164902526

x∈R


We add all the numbers together, and all the variables

(0.16+x^2)/(0.225-x^2)-4=0

We multiply all the terms by the denominator


(0.16+x^2)-4*(0.225-x^2)=0

We multiply parentheses

(0.16+x^2)+4x^2-0.9=0

We get rid of parentheses

x^2+4x^2+0.16-0.9=0

We add all the numbers together, and all the variables

5x^2-0.74=0

a = 5; b = 0; c = -0.74;
Δ = b2-4ac
Δ = 02-4·5·(-0.74)
Δ = 14.8
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)-\sqrt{14.8}}{2*5}=\frac{0-\sqrt{14.8}}{10}
=-\frac{\sqrt{}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+\sqrt{14.8}}{2*5}=\frac{0+\sqrt{14.8}}{10}
=\frac{\sqrt{}}{10}
$