34x-12=1/2x-6

Solution for 34x-12=1/2x-6 equation:

34x-12=1/2x-6

We move all terms to the left:

34x-12-(1/2x-6)=0


Domain of the equation: 2x-6)!=0

x∈R


We get rid of parentheses

34x-1/2x+6-12=0

We multiply all the terms by the denominator


34x*2x+6*2x-12*2x-1=0

Wy multiply elements

68x^2+12x-24x-1=0

We add all the numbers together, and all the variables

68x^2-12x-1=0

a = 68; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·68·(-1)
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{26}}{2*68}=\frac{12-4\sqrt{26}}{136}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{26}}{2*68}=\frac{12+4\sqrt{26}}{136}
$