x+x+1/4x+1/4x=180

Solution for x+x+1/4x+1/4x=180 equation:

x+x+1/4x+1/4x=180

We move all terms to the left:

x+x+1/4x+1/4x-(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

2x+1/4x+1/4x-180=0

We multiply all the terms by the denominator


2x*4x-180*4x+1+1=0

We add all the numbers together, and all the variables

2x*4x-180*4x+2=0

Wy multiply elements

8x^2-720x+2=0

a = 8; b = -720; c = +2;
Δ = b2-4ac
Δ = -7202-4·8·2
Δ = 518336
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:

$\sqrt{\Delta}=\sqrt{518336}=\sqrt{64*8099}=\sqrt{64}*\sqrt{8099}=8\sqrt{8099}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-720)-8\sqrt{8099}}{2*8}=\frac{720-8\sqrt{8099}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-720)+8\sqrt{8099}}{2*8}=\frac{720+8\sqrt{8099}}{16}
$