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3(2x-1)(2x+3)=-24x
We move all terms to the left:
3(2x-1)(2x+3)-(-24x)=0
We get rid of parentheses
3(2x-1)(2x+3)+24x=0
We multiply parentheses ..
3(+4x^2+6x-2x-3)+24x=0
We multiply parentheses
12x^2+18x-6x+24x-9=0
We add all the numbers together, and all the variables
12x^2+36x-9=0
a = 12; b = 36; c = -9;
Δ = b2-4ac
Δ = 362-4·12·(-9)
Δ = 1728
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-24\sqrt{3}}{2*12}=\frac{-36-24\sqrt{3}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+24\sqrt{3}}{2*12}=\frac{-36+24\sqrt{3}}{24} $
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