Y=4/x+x+0.2-5x

Solution for Y=4/x+x+0.2-5x equation:

=4/Y+Y+0.2-5Y

We move all terms to the left:

-(4/Y+Y+0.2-5Y)=0


Domain of the equation: Y+Y+0.2-5Y)!=0

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

Y+Y-5Y)!=-0.2

Y∈R


We add all the numbers together, and all the variables

-(-4Y+4/Y+0.2)=0

We get rid of parentheses

4Y-4/Y-0.2=0

We multiply all the terms by the denominator


4Y*Y-(0.2)*Y-4=0

We multiply parentheses

4Y*Y-0.2Y-4=0

Wy multiply elements

4Y^2-0.2Y-4=0

a = 4; b = -0.2; c = -4;
Δ = b2-4ac
Δ = -0.22-4·4·(-4)
Δ = 64.04
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.2)-\sqrt{64.04}}{2*4}=\frac{0.2-\sqrt{64.04}}{8}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.2)+\sqrt{64.04}}{2*4}=\frac{0.2+\sqrt{64.04}}{8}
$