2/x+4.5+6x=52

Solution for 2/x+4.5+6x=52 equation:

2/x+4.5+6x=52

We move all terms to the left:

2/x+4.5+6x-(52)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

6x+2/x-47.5=0

We multiply all the terms by the denominator


6x*x-(47.5)*x+2=0

We multiply parentheses

6x*x-47.5x+2=0

Wy multiply elements

6x^2-47.5x+2=0

a = 6; b = -47.5; c = +2;
Δ = b2-4ac
Δ = -47.52-4·6·2
Δ = 2208.25
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{-(-47.5)-\sqrt{2208.25}}{2*6}=\frac{47.5-\sqrt{2208.25}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47.5)+\sqrt{2208.25}}{2*6}=\frac{47.5+\sqrt{2208.25}}{12}
$