1+5/8x=1/4x+10

Solution for 1+5/8x=1/4x+10 equation:

1+5/8x=1/4x+10

We move all terms to the left:

1+5/8x-(1/4x+10)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x+10)!=0

x∈R


We get rid of parentheses

5/8x-1/4x-10+1=0

We calculate fractions


20x/32x^2+(-8x)/32x^2-10+1=0

We add all the numbers together, and all the variables

20x/32x^2+(-8x)/32x^2-9=0

We multiply all the terms by the denominator


20x+(-8x)-9*32x^2=0

Wy multiply elements

-288x^2+20x+(-8x)=0

We get rid of parentheses

-288x^2+20x-8x=0

We add all the numbers together, and all the variables

-288x^2+12x=0

a = -288; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-288)·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*-288}=\frac{-24}{-576}
=1/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-288}=\frac{0}{-576}
=0
$