1/2x+4=72x-1

Solution for 1/2x+4=72x-1 equation:

1/2x+4=72x-1

We move all terms to the left:

1/2x+4-(72x-1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-72x+1+4=0

We multiply all the terms by the denominator


-72x*2x+1*2x+4*2x+1=0

Wy multiply elements

-144x^2+2x+8x+1=0

We add all the numbers together, and all the variables

-144x^2+10x+1=0

a = -144; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·(-144)·1
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-26}{2*-144}=\frac{-36}{-288}
=1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+26}{2*-144}=\frac{16}{-288}
=-1/18
$