45/4x+2x=190

Solution for 45/4x+2x=190 equation:

45/4x+2x=190

We move all terms to the left:

45/4x+2x-(190)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

2x+45/4x-190=0

We multiply all the terms by the denominator


2x*4x-190*4x+45=0

Wy multiply elements

8x^2-760x+45=0

a = 8; b = -760; c = +45;
Δ = b2-4ac
Δ = -7602-4·8·45
Δ = 576160
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:

$\sqrt{\Delta}=\sqrt{576160}=\sqrt{16*36010}=\sqrt{16}*\sqrt{36010}=4\sqrt{36010}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-760)-4\sqrt{36010}}{2*8}=\frac{760-4\sqrt{36010}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-760)+4\sqrt{36010}}{2*8}=\frac{760+4\sqrt{36010}}{16}
$