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

Simple and best practice solution for (4x+3)/(2x+5)=x equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

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 $

See similar equations:

| x/7+1=5 | | 81x²-1=0 | | 3x÷5=15 | | 4(3-6x)=-2(x=5) | | x-8=x/2-x/3-6/3 | | x-8=(x/2)-(x-6/3) | | 5/6+y=3/5 | | x-8=(x/2)-(x/3-6/3) | | 5.3=9.5+0.7x | | -3(y+3)=2y3 | | 11/x+5=3 | | 120=37.27+.25x | | 6x+7=13x+7 | | x-8=(x/2)-(x-6)/3 | | 81(x.x)-1=0 | | 4/15x=9/15+4/10x | | x/12+6=8 | | 2*9.81*10=0.5*2*v^2 | | 3/2y-2=3/5 | | 8+7(x-4)=3(x+4) | | 81x.x-1=0 | | –10+8x–7x+10=x+6–x–6 | | 2–3(x–1)=13 | | (x-4)^2-4=0 | | 8x+9/x-11=10 | | 4.2−1.4y=2.1 | | 3zz=1.2 | | 1/9-4y=4 | | A(x)=20x-0,5x2 | | -4.7-3x=0.7 | | 6x+29=3x+92 | | 2/7-7x=-7x+4/7 |

Equations solver categories