2x+6/4x-4=0

Solution for 2x+6/4x-4=0 equation:

2x+6/4x-4=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

8x^2-16x+6=0

a = 8; b = -16; c = +6;
Δ = b2-4ac
Δ = -162-4·8·6
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8}{2*8}=\frac{8}{16}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8}{2*8}=\frac{24}{16}
=1+1/2
$