2x+15=4x-5/3(x)

Solution for 2x+15=4x-5/3(x) equation:

2x+15=4x-5/3(x)

We move all terms to the left:

2x+15-(4x-5/3(x))=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+4x-5/3x)+15=0

We get rid of parentheses

2x-4x+5/3x+15=0

We multiply all the terms by the denominator


2x*3x-4x*3x+15*3x+5=0

Wy multiply elements

6x^2-12x^2+45x+5=0

We add all the numbers together, and all the variables

-6x^2+45x+5=0

a = -6; b = 45; c = +5;
Δ = b2-4ac
Δ = 452-4·(-6)·5
Δ = 2145
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{-(45)-\sqrt{2145}}{2*-6}=\frac{-45-\sqrt{2145}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2145}}{2*-6}=\frac{-45+\sqrt{2145}}{-12}
$