2/3x+5=13x+15

Solution for 2/3x+5=13x+15 equation:

2/3x+5=13x+15

We move all terms to the left:

2/3x+5-(13x+15)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-13x-15+5=0

We multiply all the terms by the denominator


-13x*3x-15*3x+5*3x+2=0

Wy multiply elements

-39x^2-45x+15x+2=0

We add all the numbers together, and all the variables

-39x^2-30x+2=0

a = -39; b = -30; c = +2;
Δ = b2-4ac
Δ = -302-4·(-39)·2
Δ = 1212
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:

$\sqrt{\Delta}=\sqrt{1212}=\sqrt{4*303}=\sqrt{4}*\sqrt{303}=2\sqrt{303}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{303}}{2*-39}=\frac{30-2\sqrt{303}}{-78}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{303}}{2*-39}=\frac{30+2\sqrt{303}}{-78}
$