2/3x-15=4x+13

Solution for 2/3x-15=4x+13 equation:

2/3x-15=4x+13

We move all terms to the left:

2/3x-15-(4x+13)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-4x-13-15=0

We multiply all the terms by the denominator


-4x*3x-13*3x-15*3x+2=0

Wy multiply elements

-12x^2-39x-45x+2=0

We add all the numbers together, and all the variables

-12x^2-84x+2=0

a = -12; b = -84; c = +2;
Δ = b2-4ac
Δ = -842-4·(-12)·2
Δ = 7152
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:

$\sqrt{\Delta}=\sqrt{7152}=\sqrt{16*447}=\sqrt{16}*\sqrt{447}=4\sqrt{447}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-4\sqrt{447}}{2*-12}=\frac{84-4\sqrt{447}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+4\sqrt{447}}{2*-12}=\frac{84+4\sqrt{447}}{-24}
$