(4x+3)/(2x+5)=x

Solution for (4x+3)/(2x+5)=x equation:

(4x+3)/(2x+5)=x

We move all terms to the left:

(4x+3)/(2x+5)-(x)=0


Domain of the equation: (2x+5)!=0

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

2x!=-5

x!=-5/2

x!=-2+1/2

x∈R


We add all the numbers together, and all the variables

-1x+(4x+3)/(2x+5)=0

We multiply all the terms by the denominator


-1x*(2x+5)+(4x+3)=0

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = -1; c = +3;
Δ = b2-4ac
Δ = -12-4·(-2)·3
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5}{2*-2}=\frac{-4}{-4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5}{2*-2}=\frac{6}{-4}
=-1+1/2
$