(5/4x)+x=180

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

(5/4x)+x=180

We move all terms to the left:

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


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

x+5/4x-180=0

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2-720x+5=0

a = 4; b = -720; c = +5;
Δ = b2-4ac
Δ = -7202-4·4·5
Δ = 518320
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:

$\sqrt{\Delta}=\sqrt{518320}=\sqrt{16*32395}=\sqrt{16}*\sqrt{32395}=4\sqrt{32395}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-720)-4\sqrt{32395}}{2*4}=\frac{720-4\sqrt{32395}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-720)+4\sqrt{32395}}{2*4}=\frac{720+4\sqrt{32395}}{8}
$