4x-(1/2x-1)=14

Solution for 4x-(1/2x-1)=14 equation:

4x-(1/2x-1)=14

We move all terms to the left:

4x-(1/2x-1)-(14)=0


Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

4x-1/2x+1-14=0

We multiply all the terms by the denominator


4x*2x+1*2x-14*2x-1=0

Wy multiply elements

8x^2+2x-28x-1=0

We add all the numbers together, and all the variables

8x^2-26x-1=0

a = 8; b = -26; c = -1;
Δ = b2-4ac
Δ = -262-4·8·(-1)
Δ = 708
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:

$\sqrt{\Delta}=\sqrt{708}=\sqrt{4*177}=\sqrt{4}*\sqrt{177}=2\sqrt{177}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{177}}{2*8}=\frac{26-2\sqrt{177}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{177}}{2*8}=\frac{26+2\sqrt{177}}{16}
$