2x+1/4x-19=180

Solution for 2x+1/4x-19=180 equation:

2x+1/4x-19=180

We move all terms to the left:

2x+1/4x-19-(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-199=0

We multiply all the terms by the denominator


2x*4x-199*4x+1=0

Wy multiply elements

8x^2-796x+1=0

a = 8; b = -796; c = +1;
Δ = b2-4ac
Δ = -7962-4·8·1
Δ = 633584
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:

$\sqrt{\Delta}=\sqrt{633584}=\sqrt{16*39599}=\sqrt{16}*\sqrt{39599}=4\sqrt{39599}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-796)-4\sqrt{39599}}{2*8}=\frac{796-4\sqrt{39599}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-796)+4\sqrt{39599}}{2*8}=\frac{796+4\sqrt{39599}}{16}
$