(x+1)(3-2x)=4x2-9

Solution for (x+1)(3-2x)=4x2-9 equation:

(x+1)(3-2x)=4x^2-9

We move all terms to the left:

(x+1)(3-2x)-(4x^2-9)=0

We add all the numbers together, and all the variables

(x+1)(-2x+3)-(4x^2-9)=0

We get rid of parentheses

-4x^2+(x+1)(-2x+3)+9=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-6x^2+x+12=0

a = -6; b = 1; c = +12;
Δ = b2-4ac
Δ = 12-4·(-6)·12
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-17}{2*-6}=\frac{-18}{-12}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+17}{2*-6}=\frac{16}{-12}
=-1+1/3
$