2/3x+11=14x-13

Solution for 2/3x+11=14x-13 equation:

2/3x+11=14x-13

We move all terms to the left:

2/3x+11-(14x-13)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-14x+13+11=0

We multiply all the terms by the denominator


-14x*3x+13*3x+11*3x+2=0

Wy multiply elements

-42x^2+39x+33x+2=0

We add all the numbers together, and all the variables

-42x^2+72x+2=0

a = -42; b = 72; c = +2;
Δ = b2-4ac
Δ = 722-4·(-42)·2
Δ = 5520
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:

$\sqrt{\Delta}=\sqrt{5520}=\sqrt{16*345}=\sqrt{16}*\sqrt{345}=4\sqrt{345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-4\sqrt{345}}{2*-42}=\frac{-72-4\sqrt{345}}{-84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+4\sqrt{345}}{2*-42}=\frac{-72+4\sqrt{345}}{-84}
$