2/3x-14=x+13

Solution for 2/3x-14=x+13 equation:

2/3x-14=x+13

We move all terms to the left:

2/3x-14-(x+13)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-x-13-14=0

We multiply all the terms by the denominator


-x*3x-13*3x-14*3x+2=0

Wy multiply elements

-3x^2-39x-42x+2=0

We add all the numbers together, and all the variables

-3x^2-81x+2=0

a = -3; b = -81; c = +2;
Δ = b2-4ac
Δ = -812-4·(-3)·2
Δ = 6585
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-\sqrt{6585}}{2*-3}=\frac{81-\sqrt{6585}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+\sqrt{6585}}{2*-3}=\frac{81+\sqrt{6585}}{-6}
$