2x=45/x=90

Solution for 2x=45/x=90 equation:

2x=45/x=90

We move all terms to the left:

2x-(45/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+45/x)=0

We get rid of parentheses

2x-45/x=0

We multiply all the terms by the denominator


2x*x-45=0

Wy multiply elements

2x^2-45=0

a = 2; b = 0; c = -45;
Δ = b2-4ac
Δ = 02-4·2·(-45)
Δ = 360
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{10}}{2*2}=\frac{0-6\sqrt{10}}{4}
=-\frac{6\sqrt{10}}{4}
=-\frac{3\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{10}}{2*2}=\frac{0+6\sqrt{10}}{4}
=\frac{6\sqrt{10}}{4}
=\frac{3\sqrt{10}}{2}
$