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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

4x^2-14x+1=0

a = 4; b = -14; c = +1;
Δ = b2-4ac
Δ = -142-4·4·1
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6\sqrt{5}}{2*4}=\frac{14-6\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6\sqrt{5}}{2*4}=\frac{14+6\sqrt{5}}{8}
$