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6x(4+2x)=12
We move all terms to the left:
6x(4+2x)-(12)=0
We add all the numbers together, and all the variables
6x(2x+4)-12=0
We multiply parentheses
12x^2+24x-12=0
a = 12; b = 24; c = -12;
Δ = b2-4ac
Δ = 242-4·12·(-12)
Δ = 1152
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24\sqrt{2}}{2*12}=\frac{-24-24\sqrt{2}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24\sqrt{2}}{2*12}=\frac{-24+24\sqrt{2}}{24} $
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