-.333333333x+34=5/6x+13

Solution for -.333333333x+34=5/6x+13 equation:

-.333333333x+34=5/6x+13

We move all terms to the left:

-.333333333x+34-(5/6x+13)=0


Domain of the equation: 6x+13)!=0

x∈R


We add all the numbers together, and all the variables

-0.333333333x-(5/6x+13)+34=0

We get rid of parentheses

-0.333333333x-5/6x-13+34=0

We multiply all the terms by the denominator


-(0.333333333x)*6x-13*6x+34*6x-5=0

We add all the numbers together, and all the variables

-(+0.333333333x)*6x-13*6x+34*6x-5=0

We multiply parentheses

-0x^2-13*6x+34*6x-5=0

Wy multiply elements

-0x^2-78x+204x-5=0

We add all the numbers together, and all the variables

-1x^2+126x-5=0

a = -1; b = 126; c = -5;
Δ = b2-4ac
Δ = 1262-4·(-1)·(-5)
Δ = 15856
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:

$\sqrt{\Delta}=\sqrt{15856}=\sqrt{16*991}=\sqrt{16}*\sqrt{991}=4\sqrt{991}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-4\sqrt{991}}{2*-1}=\frac{-126-4\sqrt{991}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+4\sqrt{991}}{2*-1}=\frac{-126+4\sqrt{991}}{-2}
$