x/2x+15=2x-15

Solution for x/2x+15=2x-15 equation:

x/2x+15=2x-15

We move all terms to the left:

x/2x+15-(2x-15)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

x/2x-2x+15+15=0

We multiply all the terms by the denominator


x-2x*2x+15*2x+15*2x=0

Wy multiply elements

-4x^2+x+30x+30x=0

We add all the numbers together, and all the variables

-4x^2+61x=0

a = -4; b = 61; c = 0;
Δ = b2-4ac
Δ = 612-4·(-4)·0
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(61)-61}{2*-4}=\frac{-122}{-8}
=15+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(61)+61}{2*-4}=\frac{0}{-8}
=0
$