x/2x+3=9x-11

Solution for x/2x+3=9x-11 equation:

x/2x+3=9x-11

We move all terms to the left:

x/2x+3-(9x-11)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

x/2x-9x+11+3=0

We multiply all the terms by the denominator


x-9x*2x+11*2x+3*2x=0

Wy multiply elements

-18x^2+x+22x+6x=0

We add all the numbers together, and all the variables

-18x^2+29x=0

a = -18; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-18)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*-18}=\frac{-58}{-36}
=1+11/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-18}=\frac{0}{-36}
=0
$