5(2x-3)+3x=3+7/3(x)

Solution for 5(2x-3)+3x=3+7/3(x) equation:

5(2x-3)+3x=3+7/3(x)

We move all terms to the left:

5(2x-3)+3x-(3+7/3(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

5(2x-3)+3x-(7/3x+3)=0

We add all the numbers together, and all the variables

3x+5(2x-3)-(7/3x+3)=0

We multiply parentheses

3x+10x-(7/3x+3)-15=0

We get rid of parentheses

3x+10x-7/3x-3-15=0

We multiply all the terms by the denominator


3x*3x+10x*3x-3*3x-15*3x-7=0

Wy multiply elements

9x^2+30x^2-9x-45x-7=0

We add all the numbers together, and all the variables

39x^2-54x-7=0

a = 39; b = -54; c = -7;
Δ = b2-4ac
Δ = -542-4·39·(-7)
Δ = 4008
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:

$\sqrt{\Delta}=\sqrt{4008}=\sqrt{4*1002}=\sqrt{4}*\sqrt{1002}=2\sqrt{1002}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{1002}}{2*39}=\frac{54-2\sqrt{1002}}{78}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{1002}}{2*39}=\frac{54+2\sqrt{1002}}{78}
$