1/2x-17=-6x+4

Solution for 1/2x-17=-6x+4 equation:

1/2x-17=-6x+4

We move all terms to the left:

1/2x-17-(-6x+4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x+6x-4-17=0

We multiply all the terms by the denominator


6x*2x-4*2x-17*2x+1=0

Wy multiply elements

12x^2-8x-34x+1=0

We add all the numbers together, and all the variables

12x^2-42x+1=0

a = 12; b = -42; c = +1;
Δ = b2-4ac
Δ = -422-4·12·1
Δ = 1716
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:

$\sqrt{\Delta}=\sqrt{1716}=\sqrt{4*429}=\sqrt{4}*\sqrt{429}=2\sqrt{429}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{429}}{2*12}=\frac{42-2\sqrt{429}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{429}}{2*12}=\frac{42+2\sqrt{429}}{24}
$