1/2x-2=4x-3

Solution for 1/2x-2=4x-3 equation:

1/2x-2=4x-3

We move all terms to the left:

1/2x-2-(4x-3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-4x+3-2=0

We multiply all the terms by the denominator


-4x*2x+3*2x-2*2x+1=0

Wy multiply elements

-8x^2+6x-4x+1=0

We add all the numbers together, and all the variables

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

a = -8; b = 2; c = +1;
Δ = b2-4ac
Δ = 22-4·(-8)·1
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6}{2*-8}=\frac{-8}{-16}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6}{2*-8}=\frac{4}{-16}
=-1/4
$