2/3x+9=3x-25

Solution for 2/3x+9=3x-25 equation:

2/3x+9=3x-25

We move all terms to the left:

2/3x+9-(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+9=0

We multiply all the terms by the denominator


-3x*3x+25*3x+9*3x+2=0

Wy multiply elements

-9x^2+75x+27x+2=0

We add all the numbers together, and all the variables

-9x^2+102x+2=0

a = -9; b = 102; c = +2;
Δ = b2-4ac
Δ = 1022-4·(-9)·2
Δ = 10476
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:

$\sqrt{\Delta}=\sqrt{10476}=\sqrt{36*291}=\sqrt{36}*\sqrt{291}=6\sqrt{291}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(102)-6\sqrt{291}}{2*-9}=\frac{-102-6\sqrt{291}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(102)+6\sqrt{291}}{2*-9}=\frac{-102+6\sqrt{291}}{-18}
$