X/2x-11=7x+6

Solution for X/2x-11=7x+6 equation:

X/2X-11=7X+6

We move all terms to the left:

X/2X-11-(7X+6)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We get rid of parentheses

X/2X-7X-6-11=0

We multiply all the terms by the denominator


X-7X*2X-6*2X-11*2X=0

Wy multiply elements

-14X^2+X-12X-22X=0

We add all the numbers together, and all the variables

-14X^2-33X=0

a = -14; b = -33; c = 0;
Δ = b2-4ac
Δ = -332-4·(-14)·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-33}{2*-14}=\frac{0}{-28}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+33}{2*-14}=\frac{66}{-28}
=-2+5/14
$