(2x+3)(2x+3)=-9x+27

Solution for (2x+3)(2x+3)=-9x+27 equation:

(2x+3)(2x+3)=-9x+27

We move all terms to the left:

(2x+3)(2x+3)-(-9x+27)=0

We get rid of parentheses

(2x+3)(2x+3)+9x-27=0

We multiply parentheses ..

(+4x^2+6x+6x+9)+9x-27=0

We get rid of parentheses

4x^2+6x+6x+9x+9-27=0

We add all the numbers together, and all the variables

4x^2+21x-18=0

a = 4; b = 21; c = -18;
Δ = b2-4ac
Δ = 212-4·4·(-18)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-27}{2*4}=\frac{-48}{8}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+27}{2*4}=\frac{6}{8}
=3/4
$