8/3x=2x+14

Solution for 8/3x=2x+14 equation:

8/3x=2x+14

We move all terms to the left:

8/3x-(2x+14)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

8/3x-2x-14=0

We multiply all the terms by the denominator


-2x*3x-14*3x+8=0

Wy multiply elements

-6x^2-42x+8=0

a = -6; b = -42; c = +8;
Δ = b2-4ac
Δ = -422-4·(-6)·8
Δ = 1956
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1956}=\sqrt{4*489}=\sqrt{4}*\sqrt{489}=2\sqrt{489}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{489}}{2*-6}=\frac{42-2\sqrt{489}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{489}}{2*-6}=\frac{42+2\sqrt{489}}{-12}
$