x/2x-11=7x+16

Solution for x/2x-11=7x+16 equation:

x/2x-11=7x+16

We move all terms to the left:

x/2x-11-(7x+16)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

x/2x-7x-16-11=0

We multiply all the terms by the denominator


x-7x*2x-16*2x-11*2x=0

Wy multiply elements

-14x^2+x-32x-22x=0

We add all the numbers together, and all the variables

-14x^2-53x=0

a = -14; b = -53; c = 0;
Δ = b2-4ac
Δ = -532-4·(-14)·0
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-53}{2*-14}=\frac{0}{-28}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+53}{2*-14}=\frac{106}{-28}
=-3+11/14
$