1/2x-38=17+6x

Solution for 1/2x-38=17+6x equation:

1/2x-38=17+6x

We move all terms to the left:

1/2x-38-(17+6x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(6x+17)-38=0

We get rid of parentheses

1/2x-6x-17-38=0

We multiply all the terms by the denominator


-6x*2x-17*2x-38*2x+1=0

Wy multiply elements

-12x^2-34x-76x+1=0

We add all the numbers together, and all the variables

-12x^2-110x+1=0

a = -12; b = -110; c = +1;
Δ = b2-4ac
Δ = -1102-4·(-12)·1
Δ = 12148
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:

$\sqrt{\Delta}=\sqrt{12148}=\sqrt{4*3037}=\sqrt{4}*\sqrt{3037}=2\sqrt{3037}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-2\sqrt{3037}}{2*-12}=\frac{110-2\sqrt{3037}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+2\sqrt{3037}}{2*-12}=\frac{110+2\sqrt{3037}}{-24}
$