1/4x+x+20=180

Solution for 1/4x+x+20=180 equation:

1/4x+x+20=180

We move all terms to the left:

1/4x+x+20-(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

x+1/4x-160=0

We multiply all the terms by the denominator


x*4x-160*4x+1=0

Wy multiply elements

4x^2-640x+1=0

a = 4; b = -640; c = +1;
Δ = b2-4ac
Δ = -6402-4·4·1
Δ = 409584
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:

$\sqrt{\Delta}=\sqrt{409584}=\sqrt{16*25599}=\sqrt{16}*\sqrt{25599}=4\sqrt{25599}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-640)-4\sqrt{25599}}{2*4}=\frac{640-4\sqrt{25599}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-640)+4\sqrt{25599}}{2*4}=\frac{640+4\sqrt{25599}}{8}
$