45+7/4x+5x=180

Solution for 45+7/4x+5x=180 equation:

45+7/4x+5x=180

We move all terms to the left:

45+7/4x+5x-(180)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

5x+7/4x-135=0

We multiply all the terms by the denominator


5x*4x-135*4x+7=0

Wy multiply elements

20x^2-540x+7=0

a = 20; b = -540; c = +7;
Δ = b2-4ac
Δ = -5402-4·20·7
Δ = 291040
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:

$\sqrt{\Delta}=\sqrt{291040}=\sqrt{16*18190}=\sqrt{16}*\sqrt{18190}=4\sqrt{18190}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-4\sqrt{18190}}{2*20}=\frac{540-4\sqrt{18190}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+4\sqrt{18190}}{2*20}=\frac{540+4\sqrt{18190}}{40}
$