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(2x-1)(2x+3)=6
We move all terms to the left:
(2x-1)(2x+3)-(6)=0
We multiply parentheses ..
(+4x^2+6x-2x-3)-6=0
We get rid of parentheses
4x^2+6x-2x-3-6=0
We add all the numbers together, and all the variables
4x^2+4x-9=0
a = 4; b = 4; c = -9;
Δ = b2-4ac
Δ = 42-4·4·(-9)
Δ = 160
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{10}}{2*4}=\frac{-4-4\sqrt{10}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{10}}{2*4}=\frac{-4+4\sqrt{10}}{8} $
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