x/2x-11=5x+10x=-17x=3x=-7x=13

Solution for x/2x-11=5x+10x=-17x=3x=-7x=13 equation:

x/2x-11=5x+10x=-17x=3x=-7x=13

We move all terms to the left:

x/2x-11-(5x+10x)=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-(+15x)-11=0

We get rid of parentheses

x/2x-15x-11=0

We multiply all the terms by the denominator


x-15x*2x-11*2x=0

Wy multiply elements

-30x^2+x-22x=0

We add all the numbers together, and all the variables

-30x^2-21x=0

a = -30; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·(-30)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*-30}=\frac{0}{-60}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*-30}=\frac{42}{-60}
=-7/10
$