-5x+13=1/6x+17

Solution for -5x+13=1/6x+17 equation:

-5x+13=1/6x+17

We move all terms to the left:

-5x+13-(1/6x+17)=0


Domain of the equation: 6x+17)!=0

x∈R


We get rid of parentheses

-5x-1/6x-17+13=0

We multiply all the terms by the denominator


-5x*6x-17*6x+13*6x-1=0

Wy multiply elements

-30x^2-102x+78x-1=0

We add all the numbers together, and all the variables

-30x^2-24x-1=0

a = -30; b = -24; c = -1;
Δ = b2-4ac
Δ = -242-4·(-30)·(-1)
Δ = 456
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:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{114}}{2*-30}=\frac{24-2\sqrt{114}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{114}}{2*-30}=\frac{24+2\sqrt{114}}{-60}
$