x/2x+4=10+5x

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

x/2x+4=10+5x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-10x^2+x-20x+8x=0

We add all the numbers together, and all the variables

-10x^2-11x=0

a = -10; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-10)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*-10}=\frac{0}{-20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-10}=\frac{22}{-20}
=-1+1/10
$