(1/4x)+x+(x-81)=180

Solution for (1/4x)+x+(x-81)=180 equation:

(1/4x)+x+(x-81)=180

We move all terms to the left:

(1/4x)+x+(x-81)-(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

(+1/4x)+x+(x-81)-180=0

We add all the numbers together, and all the variables

x+(+1/4x)+(x-81)-180=0

We get rid of parentheses

x+1/4x+x-81-180=0

We multiply all the terms by the denominator


x*4x+x*4x-81*4x-180*4x+1=0

Wy multiply elements

4x^2+4x^2-324x-720x+1=0

We add all the numbers together, and all the variables

8x^2-1044x+1=0

a = 8; b = -1044; c = +1;
Δ = b2-4ac
Δ = -10442-4·8·1
Δ = 1089904
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:

$\sqrt{\Delta}=\sqrt{1089904}=\sqrt{16*68119}=\sqrt{16}*\sqrt{68119}=4\sqrt{68119}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1044)-4\sqrt{68119}}{2*8}=\frac{1044-4\sqrt{68119}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1044)+4\sqrt{68119}}{2*8}=\frac{1044+4\sqrt{68119}}{16}
$