2/x+2.25=3.6+4x

Solution for 2/x+2.25=3.6+4x equation:

2/x+2.25=3.6+4x

We move all terms to the left:

2/x+2.25-(3.6+4x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2/x-(4x+3.6)+2.25=0

We get rid of parentheses

2/x-4x-3.6+2.25=0

We multiply all the terms by the denominator


-4x*x-(3.6)*x+(2.25)*x+2=0

We multiply parentheses

-4x*x-3.6x+2.25x+2=0

Wy multiply elements

-4x^2-3.6x+2.25x+2=0

We add all the numbers together, and all the variables

-4x^2-1.35x+2=0

a = -4; b = -1.35; c = +2;
Δ = b2-4ac
Δ = -1.352-4·(-4)·2
Δ = 33.8225
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{-(-1.35)-\sqrt{33.8225}}{2*-4}=\frac{1.35-\sqrt{33.8225}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.35)+\sqrt{33.8225}}{2*-4}=\frac{1.35+\sqrt{33.8225}}{-8}
$