4x-12/2x-6=0

Solution for 4x-12/2x-6=0 equation:

4x-12/2x-6=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


4x*2x-6*2x-12=0

Wy multiply elements

8x^2-12x-12=0

a = 8; b = -12; c = -12;
Δ = b2-4ac
Δ = -122-4·8·(-12)
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{33}}{2*8}=\frac{12-4\sqrt{33}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{33}}{2*8}=\frac{12+4\sqrt{33}}{16}
$