4x*x-9=-(2x+3)(x-2)

Solution for 4x*x-9=-(2x+3)(x-2) equation:

4x*x-9=-(2x+3)(x-2)

We move all terms to the left:

4x*x-9-(-(2x+3)(x-2))=0

Wy multiply elements

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

We multiply parentheses ..

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


We calculate terms in parentheses: -(-(+2x^2-4x+3x-6)), so:

-(+2x^2-4x+3x-6)

We get rid of parentheses

-2x^2+4x-3x+6

We add all the numbers together, and all the variables

-2x^2+x+6

Back to the equation:

-(-2x^2+x+6)


We get rid of parentheses

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

We add all the numbers together, and all the variables

6x^2-1x-15=0

a = 6; b = -1; c = -15;
Δ = b2-4ac
Δ = -12-4·6·(-15)
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{-(-1)-19}{2*6}=\frac{-18}{12}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+19}{2*6}=\frac{20}{12}
=1+2/3
$