-1/2x+19=-1/4x+54

Solution for -1/2x+19=-1/4x+54 equation:

-1/2x+19=-1/4x+54

We move all terms to the left:

-1/2x+19-(-1/4x+54)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x+54)!=0

x∈R


We get rid of parentheses

-1/2x+1/4x-54+19=0

We calculate fractions


(-4x)/8x^2+2x/8x^2-54+19=0

We add all the numbers together, and all the variables

(-4x)/8x^2+2x/8x^2-35=0

We multiply all the terms by the denominator


(-4x)+2x-35*8x^2=0

We add all the numbers together, and all the variables

2x+(-4x)-35*8x^2=0

Wy multiply elements

-280x^2+2x+(-4x)=0

We get rid of parentheses

-280x^2+2x-4x=0

We add all the numbers together, and all the variables

-280x^2-2x=0

a = -280; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-280)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-280}=\frac{0}{-560}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-280}=\frac{4}{-560}
=-1/140
$