2x+6/4x=180

Solution for 2x+6/4x=180 equation:

2x+6/4x=180

We move all terms to the left:

2x+6/4x-(180)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


2x*4x-180*4x+6=0

Wy multiply elements

8x^2-720x+6=0

a = 8; b = -720; c = +6;
Δ = b2-4ac
Δ = -7202-4·8·6
Δ = 518208
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:

$\sqrt{\Delta}=\sqrt{518208}=\sqrt{64*8097}=\sqrt{64}*\sqrt{8097}=8\sqrt{8097}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-720)-8\sqrt{8097}}{2*8}=\frac{720-8\sqrt{8097}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-720)+8\sqrt{8097}}{2*8}=\frac{720+8\sqrt{8097}}{16}
$