5x+5/4x=180

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

5x+5/4x=180

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


5x*4x-180*4x+5=0

Wy multiply elements

20x^2-720x+5=0

a = 20; b = -720; c = +5;
Δ = b2-4ac
Δ = -7202-4·20·5
Δ = 518000
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:

$\sqrt{\Delta}=\sqrt{518000}=\sqrt{400*1295}=\sqrt{400}*\sqrt{1295}=20\sqrt{1295}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-720)-20\sqrt{1295}}{2*20}=\frac{720-20\sqrt{1295}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-720)+20\sqrt{1295}}{2*20}=\frac{720+20\sqrt{1295}}{40}
$