1/4x+2=5/8x-5

Solution for 1/4x+2=5/8x-5 equation:

1/4x+2=5/8x-5

We move all terms to the left:

1/4x+2-(5/8x-5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x-5)!=0

x∈R


We get rid of parentheses

1/4x-5/8x+5+2=0

We calculate fractions


8x/32x^2+(-20x)/32x^2+5+2=0

We add all the numbers together, and all the variables

8x/32x^2+(-20x)/32x^2+7=0

We multiply all the terms by the denominator


8x+(-20x)+7*32x^2=0

Wy multiply elements

224x^2+8x+(-20x)=0

We get rid of parentheses

224x^2+8x-20x=0

We add all the numbers together, and all the variables

224x^2-12x=0

a = 224; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·224·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*224}=\frac{0}{448}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*224}=\frac{24}{448}
=3/56
$