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!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

4x+1/4x-188=0

We multiply all the terms by the denominator


4x*4x-188*4x+1=0

Wy multiply elements

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}
$