(23/14)x=x+9

Solution for (23/14)x=x+9 equation:

(23/14)x=x+9

We move all terms to the left:

(23/14)x-(x+9)=0


Domain of the equation: 14)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+23/14)x-(x+9)=0

We multiply parentheses

23x^2-(x+9)=0

We get rid of parentheses

23x^2-x-9=0

We add all the numbers together, and all the variables

23x^2-1x-9=0

a = 23; b = -1; c = -9;
Δ = b2-4ac
Δ = -12-4·23·(-9)
Δ = 829
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{829}}{2*23}=\frac{1-\sqrt{829}}{46}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{829}}{2*23}=\frac{1+\sqrt{829}}{46}
$