5(3x-8)=2/3x+4

Solution for 5(3x-8)=2/3x+4 equation:

5(3x-8)=2/3x+4

We move all terms to the left:

5(3x-8)-(2/3x+4)=0


Domain of the equation: 3x+4)!=0

x∈R


We multiply parentheses

15x-(2/3x+4)-40=0

We get rid of parentheses

15x-2/3x-4-40=0

We multiply all the terms by the denominator


15x*3x-4*3x-40*3x-2=0

Wy multiply elements

45x^2-12x-120x-2=0

We add all the numbers together, and all the variables

45x^2-132x-2=0

a = 45; b = -132; c = -2;
Δ = b2-4ac
Δ = -1322-4·45·(-2)
Δ = 17784
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:

$\sqrt{\Delta}=\sqrt{17784}=\sqrt{36*494}=\sqrt{36}*\sqrt{494}=6\sqrt{494}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-6\sqrt{494}}{2*45}=\frac{132-6\sqrt{494}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+6\sqrt{494}}{2*45}=\frac{132+6\sqrt{494}}{90}
$