(3)/(4x-5)=x

Solution for (3)/(4x-5)=x equation:

(3)/(4x-5)=x

We move all terms to the left:

(3)/(4x-5)-(x)=0


Domain of the equation: (4x-5)!=0

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

4x!=5

x!=5/4

x!=1+1/4

x∈R


We add all the numbers together, and all the variables

-1x+3/(4x-5)=0

We multiply all the terms by the denominator


-1x*(4x-5)+3=0

We multiply parentheses

-4x^2+5x+3=0

a = -4; b = 5; c = +3;
Δ = b2-4ac
Δ = 52-4·(-4)·3
Δ = 73
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{-(5)-\sqrt{73}}{2*-4}=\frac{-5-\sqrt{73}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{73}}{2*-4}=\frac{-5+\sqrt{73}}{-8}
$