(4x-8)+(1/4x)=180

Solution for (4x-8)+(1/4x)=180 equation:

(4x-8)+(1/4x)=180

We move all terms to the left:

(4x-8)+(1/4x)-(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

(4x-8)+(+1/4x)-180=0

We get rid of parentheses

4x+1/4x-8-180=0

We multiply all the terms by the denominator


4x*4x-8*4x-180*4x+1=0

Wy multiply elements

16x^2-32x-720x+1=0

We add all the numbers together, and all the variables

16x^2-752x+1=0

a = 16; b = -752; c = +1;
Δ = b2-4ac
Δ = -7522-4·16·1
Δ = 565440
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:

$\sqrt{\Delta}=\sqrt{565440}=\sqrt{64*8835}=\sqrt{64}*\sqrt{8835}=8\sqrt{8835}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-752)-8\sqrt{8835}}{2*16}=\frac{752-8\sqrt{8835}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-752)+8\sqrt{8835}}{2*16}=\frac{752+8\sqrt{8835}}{32}
$