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(2x-1)(2x+1)=4x+7
We move all terms to the left:
(2x-1)(2x+1)-(4x+7)=0
We use the square of the difference formula
4x^2-(4x+7)-1=0
We get rid of parentheses
4x^2-4x-7-1=0
We add all the numbers together, and all the variables
4x^2-4x-8=0
a = 4; b = -4; c = -8;
Δ = b2-4ac
Δ = -42-4·4·(-8)
Δ = 144
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{144}=12$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-12}{2*4}=\frac{-8}{8} =-1 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+12}{2*4}=\frac{16}{8} =2 $
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