13/3x+15=2x-8

Solution for 13/3x+15=2x-8 equation:

13/3x+15=2x-8

We move all terms to the left:

13/3x+15-(2x-8)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

13/3x-2x+8+15=0

We multiply all the terms by the denominator


-2x*3x+8*3x+15*3x+13=0

Wy multiply elements

-6x^2+24x+45x+13=0

We add all the numbers together, and all the variables

-6x^2+69x+13=0

a = -6; b = 69; c = +13;
Δ = b2-4ac
Δ = 692-4·(-6)·13
Δ = 5073
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{-(69)-\sqrt{5073}}{2*-6}=\frac{-69-\sqrt{5073}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+\sqrt{5073}}{2*-6}=\frac{-69+\sqrt{5073}}{-12}
$