1/2x-4=37-2x

Solution for 1/2x-4=37-2x equation:

1/2x-4=37-2x

We move all terms to the left:

1/2x-4-(37-2x)=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-(-2x+37)-4=0

We get rid of parentheses

1/2x+2x-37-4=0

We multiply all the terms by the denominator


2x*2x-37*2x-4*2x+1=0

Wy multiply elements

4x^2-74x-8x+1=0

We add all the numbers together, and all the variables

4x^2-82x+1=0

a = 4; b = -82; c = +1;
Δ = b2-4ac
Δ = -822-4·4·1
Δ = 6708
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:

$\sqrt{\Delta}=\sqrt{6708}=\sqrt{4*1677}=\sqrt{4}*\sqrt{1677}=2\sqrt{1677}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-2\sqrt{1677}}{2*4}=\frac{82-2\sqrt{1677}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+2\sqrt{1677}}{2*4}=\frac{82+2\sqrt{1677}}{8}
$