4x-23=1/2x-2

Solution for 4x-23=1/2x-2 equation:

4x-23=1/2x-2

We move all terms to the left:

4x-23-(1/2x-2)=0


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

x∈R


We get rid of parentheses

4x-1/2x+2-23=0

We multiply all the terms by the denominator


4x*2x+2*2x-23*2x-1=0

Wy multiply elements

8x^2+4x-46x-1=0

We add all the numbers together, and all the variables

8x^2-42x-1=0

a = 8; b = -42; c = -1;
Δ = b2-4ac
Δ = -422-4·8·(-1)
Δ = 1796
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:

$\sqrt{\Delta}=\sqrt{1796}=\sqrt{4*449}=\sqrt{4}*\sqrt{449}=2\sqrt{449}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{449}}{2*8}=\frac{42-2\sqrt{449}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{449}}{2*8}=\frac{42+2\sqrt{449}}{16}
$