2/3x+8=2x-14

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

2/3x+8=2x-14

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6x^2+42x+24x+2=0

We add all the numbers together, and all the variables

-6x^2+66x+2=0

a = -6; b = 66; c = +2;
Δ = b2-4ac
Δ = 662-4·(-6)·2
Δ = 4404
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:

$\sqrt{\Delta}=\sqrt{4404}=\sqrt{4*1101}=\sqrt{4}*\sqrt{1101}=2\sqrt{1101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-2\sqrt{1101}}{2*-6}=\frac{-66-2\sqrt{1101}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+2\sqrt{1101}}{2*-6}=\frac{-66+2\sqrt{1101}}{-12}
$