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 get rid of parentheses

-4/Y-^Y+5Y-0.2=0

We multiply all the terms by the denominator


-^Y*Y+5Y*Y-(0.2)*Y-4=0

We multiply parentheses

-^Y*Y+5Y*Y-0.2Y-4=0

Wy multiply elements

Y^2+5Y^2-0.2Y-4=0

We add all the numbers together, and all the variables

6Y^2-0.2Y-4=0

a = 6; b = -0.2; c = -4;
Δ = b2-4ac
Δ = -0.22-4·6·(-4)
Δ = 96.04
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{96.04}}{2*6}=\frac{0.2-\sqrt{96.04}}{12}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.2)+\sqrt{96.04}}{2*6}=\frac{0.2+\sqrt{96.04}}{12}
$