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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


1536x/2048x^2+12x/2048x^2+(-4x)/2048x^2-10=0

We multiply all the terms by the denominator


1536x+12x+(-4x)-10*2048x^2=0

We add all the numbers together, and all the variables

1548x+(-4x)-10*2048x^2=0

Wy multiply elements

-20480x^2+1548x+(-4x)=0

We get rid of parentheses

-20480x^2+1548x-4x=0

We add all the numbers together, and all the variables

-20480x^2+1544x=0

a = -20480; b = 1544; c = 0;
Δ = b2-4ac
Δ = 15442-4·(-20480)·0
Δ = 2383936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2383936}=1544$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1544)-1544}{2*-20480}=\frac{-3088}{-40960}
=193/2560
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1544)+1544}{2*-20480}=\frac{0}{-40960}
=0
$