10/2x+4=4x/x+5

Solution for 10/2x+4=4x/x+5 equation:

10/2x+4=4x/x+5

We move all terms to the left:

10/2x+4-(4x/x+5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

10/2x-4x/x-5+4=0

We calculate fractions


(-8x^2)/2x^2+10x/2x^2-5+4=0

We add all the numbers together, and all the variables

(-8x^2)/2x^2+10x/2x^2-1=0

We multiply all the terms by the denominator


(-8x^2)+10x-1*2x^2=0

Wy multiply elements

(-8x^2)-2x^2+10x=0

We get rid of parentheses

-8x^2-2x^2+10x=0

We add all the numbers together, and all the variables

-10x^2+10x=0

a = -10; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-10)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-10}=\frac{-20}{-20}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-10}=\frac{0}{-20}
=0
$