(5x+24)/(9x-17)=x

Solution for (5x+24)/(9x-17)=x equation:

(5x+24)/(9x-17)=x

We move all terms to the left:

(5x+24)/(9x-17)-(x)=0


Domain of the equation: (9x-17)!=0

We move all terms containing x to the left, all other terms to the right

9x!=17

x!=17/9

x!=1+8/9

x∈R


We add all the numbers together, and all the variables

-1x+(5x+24)/(9x-17)=0

We multiply all the terms by the denominator


-1x*(9x-17)+(5x+24)=0

We multiply parentheses

-9x^2+17x+(5x+24)=0

We get rid of parentheses

-9x^2+17x+5x+24=0

We add all the numbers together, and all the variables

-9x^2+22x+24=0

a = -9; b = 22; c = +24;
Δ = b2-4ac
Δ = 222-4·(-9)·24
Δ = 1348
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:

$\sqrt{\Delta}=\sqrt{1348}=\sqrt{4*337}=\sqrt{4}*\sqrt{337}=2\sqrt{337}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{337}}{2*-9}=\frac{-22-2\sqrt{337}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{337}}{2*-9}=\frac{-22+2\sqrt{337}}{-18}
$