1/8x+10=3/4x-20

Solution for 1/8x+10=3/4x-20 equation:

1/8x+10=3/4x-20

We move all terms to the left:

1/8x+10-(3/4x-20)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x-20)!=0

x∈R


We get rid of parentheses

1/8x-3/4x+20+10=0

We calculate fractions


4x/32x^2+(-24x)/32x^2+20+10=0

We add all the numbers together, and all the variables

4x/32x^2+(-24x)/32x^2+30=0

We multiply all the terms by the denominator


4x+(-24x)+30*32x^2=0

Wy multiply elements

960x^2+4x+(-24x)=0

We get rid of parentheses

960x^2+4x-24x=0

We add all the numbers together, and all the variables

960x^2-20x=0

a = 960; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·960·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*960}=\frac{0}{1920}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*960}=\frac{40}{1920}
=1/48
$