7/2x-5/6x=11

Solution for 7/2x-5/6x=11 equation:

7/2x-5/6x=11

We move all terms to the left:

7/2x-5/6x-(11)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We calculate fractions


42x/12x^2+(-10x)/12x^2-11=0

We multiply all the terms by the denominator


42x+(-10x)-11*12x^2=0

Wy multiply elements

-132x^2+42x+(-10x)=0

We get rid of parentheses

-132x^2+42x-10x=0

We add all the numbers together, and all the variables

-132x^2+32x=0

a = -132; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·(-132)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*-132}=\frac{-64}{-264}
=8/33
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*-132}=\frac{0}{-264}
=0
$