2/3x+14=13x

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

2/3x+14=13x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -39; b = 42; c = +2;
Δ = b2-4ac
Δ = 422-4·(-39)·2
Δ = 2076
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:

$\sqrt{\Delta}=\sqrt{2076}=\sqrt{4*519}=\sqrt{4}*\sqrt{519}=2\sqrt{519}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{519}}{2*-39}=\frac{-42-2\sqrt{519}}{-78}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{519}}{2*-39}=\frac{-42+2\sqrt{519}}{-78}
$