1/2x-2=11/14x+3

Solution for 1/2x-2=11/14x+3 equation:

1/2x-2=11/14x+3

We move all terms to the left:

1/2x-2-(11/14x+3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 14x+3)!=0

x∈R


We get rid of parentheses

1/2x-11/14x-3-2=0

We calculate fractions


14x/28x^2+(-22x)/28x^2-3-2=0

We add all the numbers together, and all the variables

14x/28x^2+(-22x)/28x^2-5=0

We multiply all the terms by the denominator


14x+(-22x)-5*28x^2=0

Wy multiply elements

-140x^2+14x+(-22x)=0

We get rid of parentheses

-140x^2+14x-22x=0

We add all the numbers together, and all the variables

-140x^2-8x=0

a = -140; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-140)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-140}=\frac{0}{-280}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-140}=\frac{16}{-280}
=-2/35
$