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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+9x^2+6x+6x+4)-((2x-5)(3x+2))=0


We calculate terms in parentheses: -((2x-5)(3x+2)), so:

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

We multiply parentheses ..

(+6x^2+4x-15x-10)

We get rid of parentheses

6x^2+4x-15x-10

We add all the numbers together, and all the variables

6x^2-11x-10

Back to the equation:

-(6x^2-11x-10)


We get rid of parentheses

9x^2-6x^2+6x+6x+11x+4+10=0

We add all the numbers together, and all the variables

3x^2+23x+14=0

a = 3; b = 23; c = +14;
Δ = b2-4ac
Δ = 232-4·3·14
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-19}{2*3}=\frac{-42}{6}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+19}{2*3}=\frac{-4}{6}
=-2/3
$