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(2x+3)(2x-3)=x+9
We move all terms to the left:
(2x+3)(2x-3)-(x+9)=0
We use the square of the difference formula
4x^2-(x+9)-9=0
We get rid of parentheses
4x^2-x-9-9=0
We add all the numbers together, and all the variables
4x^2-1x-18=0
a = 4; b = -1; c = -18;
Δ = b2-4ac
Δ = -12-4·4·(-18)
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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-17}{2*4}=\frac{-16}{8} =-2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+17}{2*4}=\frac{18}{8} =2+1/4 $
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