9/8x-2x+28=21/8x

Solution for 9/8x-2x+28=21/8x equation:

9/8x-2x+28=21/8x

We move all terms to the left:

9/8x-2x+28-(21/8x)=0


Domain of the equation: 8x!=0

x!=0/8

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

9/8x-2x-(+21/8x)+28=0

We add all the numbers together, and all the variables

-2x+9/8x-(+21/8x)+28=0

We get rid of parentheses

-2x+9/8x-21/8x+28=0

We multiply all the terms by the denominator


-2x*8x+28*8x+9-21=0

We add all the numbers together, and all the variables

-2x*8x+28*8x-12=0

Wy multiply elements

-16x^2+224x-12=0

a = -16; b = 224; c = -12;
Δ = b2-4ac
Δ = 2242-4·(-16)·(-12)
Δ = 49408
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{49408}=\sqrt{256*193}=\sqrt{256}*\sqrt{193}=16\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(224)-16\sqrt{193}}{2*-16}=\frac{-224-16\sqrt{193}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(224)+16\sqrt{193}}{2*-16}=\frac{-224+16\sqrt{193}}{-32}
$