(8/9)x-10/9=3

Solution for (8/9)x-10/9=3 equation:

(8/9)x-10/9=3

We move all terms to the left:

(8/9)x-10/9-(3)=0


Domain of the equation: 9)x!=0

x!=0/1

x!=0

x∈R


determiningTheFunctionDomain
(8/9)x-3-10/9=0

We add all the numbers together, and all the variables

(+8/9)x-3-10/9=0

We multiply parentheses

8x^2-3-10/9=0

We multiply all the terms by the denominator


8x^2*9-10-3*9=0

We add all the numbers together, and all the variables

8x^2*9-37=0

Wy multiply elements

72x^2-37=0

a = 72; b = 0; c = -37;
Δ = b2-4ac
Δ = 02-4·72·(-37)
Δ = 10656
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:

$\sqrt{\Delta}=\sqrt{10656}=\sqrt{144*74}=\sqrt{144}*\sqrt{74}=12\sqrt{74}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{74}}{2*72}=\frac{0-12\sqrt{74}}{144}
=-\frac{12\sqrt{74}}{144}
=-\frac{\sqrt{74}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{74}}{2*72}=\frac{0+12\sqrt{74}}{144}
=\frac{12\sqrt{74}}{144}
=\frac{\sqrt{74}}{12}
$