(3x-4)/(26-x)=x

Solution for (3x-4)/(26-x)=x equation:

(3x-4)/(26-x)=x

We move all terms to the left:

(3x-4)/(26-x)-(x)=0


Domain of the equation: (26-x)!=0

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

-x!=-26

x!=-26/-1

x!=+26

x∈R


We add all the numbers together, and all the variables

(3x-4)/(-1x+26)-x=0

We add all the numbers together, and all the variables

-1x+(3x-4)/(-1x+26)=0

We multiply all the terms by the denominator


-1x*(-1x+26)+(3x-4)=0

We multiply parentheses

1x^2-26x+(3x-4)=0

We get rid of parentheses

1x^2-26x+3x-4=0

We add all the numbers together, and all the variables

x^2-23x-4=0

a = 1; b = -23; c = -4;
Δ = b2-4ac
Δ = -232-4·1·(-4)
Δ = 545
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{-(-23)-\sqrt{545}}{2*1}=\frac{23-\sqrt{545}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{545}}{2*1}=\frac{23+\sqrt{545}}{2}
$