126-1/2x=-4+1/8x

Solution for 126-1/2x=-4+1/8x equation:

126-1/2x=-4+1/8x

We move all terms to the left:

126-1/2x-(-4+1/8x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-1/2x-(1/8x-4)+126=0

We get rid of parentheses

-1/2x-1/8x+4+126=0

We calculate fractions


(-8x)/16x^2+(-2x)/16x^2+4+126=0

We add all the numbers together, and all the variables

(-8x)/16x^2+(-2x)/16x^2+130=0

We multiply all the terms by the denominator


(-8x)+(-2x)+130*16x^2=0

Wy multiply elements

2080x^2+(-8x)+(-2x)=0

We get rid of parentheses

2080x^2-8x-2x=0

We add all the numbers together, and all the variables

2080x^2-10x=0

a = 2080; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·2080·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*2080}=\frac{0}{4160}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*2080}=\frac{20}{4160}
=1/208
$