(8/9)x=23/30

Solution for (8/9)x=23/30 equation:

(8/9)x=23/30

We move all terms to the left:

(8/9)x-(23/30)=0


Domain of the equation: 9)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+8/9)x-(+23/30)=0

We multiply parentheses

8x^2-(+23/30)=0

We get rid of parentheses

8x^2-23/30=0

We multiply all the terms by the denominator


8x^2*30-23=0

Wy multiply elements

240x^2-23=0

a = 240; b = 0; c = -23;
Δ = b2-4ac
Δ = 02-4·240·(-23)
Δ = 22080
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:

$\sqrt{\Delta}=\sqrt{22080}=\sqrt{64*345}=\sqrt{64}*\sqrt{345}=8\sqrt{345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{345}}{2*240}=\frac{0-8\sqrt{345}}{480}
=-\frac{8\sqrt{345}}{480}
=-\frac{\sqrt{345}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{345}}{2*240}=\frac{0+8\sqrt{345}}{480}
=\frac{8\sqrt{345}}{480}
=\frac{\sqrt{345}}{60}
$