-1/2+1/2x=1/5x-4

Solution for -1/2+1/2x=1/5x-4 equation:

-1/2+1/2x=1/5x-4

We move all terms to the left:

-1/2+1/2x-(1/5x-4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x-4)!=0

x∈R


We get rid of parentheses

1/2x-1/5x+4-1/2=0

We calculate fractions


5x/40x^2+(-8x)/40x^2+(-5x)/40x^2+4=0

We multiply all the terms by the denominator


5x+(-8x)+(-5x)+4*40x^2=0

Wy multiply elements

160x^2+5x+(-8x)+(-5x)=0

We get rid of parentheses

160x^2+5x-8x-5x=0

We add all the numbers together, and all the variables

160x^2-8x=0

a = 160; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·160·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*160}=\frac{0}{320}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*160}=\frac{16}{320}
=1/20
$