3/2x-4+3/8x-3/4=7/8

Solution for 3/2x-4+3/8x-3/4=7/8 equation:

3/2x-4+3/8x-3/4=7/8

We move all terms to the left:

3/2x-4+3/8x-3/4-(7/8)=0


Domain of the equation: 2x!=0

x!=0/2

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

3/2x+3/8x-4-3/4-(+7/8)=0

We get rid of parentheses

3/2x+3/8x-4-3/4-7/8=0

We calculate fractions


(-3072x^2)/2048x^2+3072x/2048x^2+96x/2048x^2+(-224x)/2048x^2-4=0

We multiply all the terms by the denominator


(-3072x^2)+3072x+96x+(-224x)-4*2048x^2=0

We add all the numbers together, and all the variables

(-3072x^2)+3168x+(-224x)-4*2048x^2=0

Wy multiply elements

(-3072x^2)-8192x^2+3168x+(-224x)=0

We get rid of parentheses

-3072x^2-8192x^2+3168x-224x=0

We add all the numbers together, and all the variables

-11264x^2+2944x=0

a = -11264; b = 2944; c = 0;
Δ = b2-4ac
Δ = 29442-4·(-11264)·0
Δ = 8667136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8667136}=2944$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2944)-2944}{2*-11264}=\frac{-5888}{-22528}
=23/88
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2944)+2944}{2*-11264}=\frac{0}{-22528}
=0
$