5x-13=-4/3x+6

Solution for 5x-13=-4/3x+6 equation:

5x-13=-4/3x+6

We move all terms to the left:

5x-13-(-4/3x+6)=0


Domain of the equation: 3x+6)!=0

x∈R


We get rid of parentheses

5x+4/3x-6-13=0

We multiply all the terms by the denominator


5x*3x-6*3x-13*3x+4=0

Wy multiply elements

15x^2-18x-39x+4=0

We add all the numbers together, and all the variables

15x^2-57x+4=0

a = 15; b = -57; c = +4;
Δ = b2-4ac
Δ = -572-4·15·4
Δ = 3009
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{-(-57)-\sqrt{3009}}{2*15}=\frac{57-\sqrt{3009}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+\sqrt{3009}}{2*15}=\frac{57+\sqrt{3009}}{30}
$