2/3x+27=3x-25

Solution for 2/3x+27=3x-25 equation:

2/3x+27=3x-25

We move all terms to the left:

2/3x+27-(3x-25)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-3x+25+27=0

We multiply all the terms by the denominator


-3x*3x+25*3x+27*3x+2=0

Wy multiply elements

-9x^2+75x+81x+2=0

We add all the numbers together, and all the variables

-9x^2+156x+2=0

a = -9; b = 156; c = +2;
Δ = b2-4ac
Δ = 1562-4·(-9)·2
Δ = 24408
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:

$\sqrt{\Delta}=\sqrt{24408}=\sqrt{36*678}=\sqrt{36}*\sqrt{678}=6\sqrt{678}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(156)-6\sqrt{678}}{2*-9}=\frac{-156-6\sqrt{678}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(156)+6\sqrt{678}}{2*-9}=\frac{-156+6\sqrt{678}}{-18}
$