2-(3)/(4)x=(5)/(8)x

Solution for 2-(3)/(4)x=(5)/(8)x equation:

2-(3)/(4)x=(5)/(8)x

We move all terms to the left:

2-(3)/(4)x-((5)/(8)x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-3/4x-(+5/8x)+2=0

We get rid of parentheses

-3/4x-5/8x+2=0

We calculate fractions


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

We multiply all the terms by the denominator


(-24x)+(-20x)+2*32x^2=0

Wy multiply elements

64x^2+(-24x)+(-20x)=0

We get rid of parentheses

64x^2-24x-20x=0

We add all the numbers together, and all the variables

64x^2-44x=0

a = 64; b = -44; c = 0;
Δ = b2-4ac
Δ = -442-4·64·0
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-44}{2*64}=\frac{0}{128}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+44}{2*64}=\frac{88}{128}
=11/16
$