2x-6/4x=36

Solution for 2x-6/4x=36 equation:

2x-6/4x=36

We move all terms to the left:

2x-6/4x-(36)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


2x*4x-36*4x-6=0

Wy multiply elements

8x^2-144x-6=0

a = 8; b = -144; c = -6;
Δ = b2-4ac
Δ = -1442-4·8·(-6)
Δ = 20928
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:

$\sqrt{\Delta}=\sqrt{20928}=\sqrt{64*327}=\sqrt{64}*\sqrt{327}=8\sqrt{327}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-8\sqrt{327}}{2*8}=\frac{144-8\sqrt{327}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+8\sqrt{327}}{2*8}=\frac{144+8\sqrt{327}}{16}
$