5x-6=2/3x+2=3

Solution for 5x-6=2/3x+2=3 equation:

5x-6=2/3x+2=3

We move all terms to the left:

5x-6-(2/3x+2)=0


Domain of the equation: 3x+2)!=0

x∈R


We get rid of parentheses

5x-2/3x-2-6=0

We multiply all the terms by the denominator


5x*3x-2*3x-6*3x-2=0

Wy multiply elements

15x^2-6x-18x-2=0

We add all the numbers together, and all the variables

15x^2-24x-2=0

a = 15; b = -24; c = -2;
Δ = b2-4ac
Δ = -242-4·15·(-2)
Δ = 696
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:

$\sqrt{\Delta}=\sqrt{696}=\sqrt{4*174}=\sqrt{4}*\sqrt{174}=2\sqrt{174}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{174}}{2*15}=\frac{24-2\sqrt{174}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{174}}{2*15}=\frac{24+2\sqrt{174}}{30}
$