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4x(1/2x+6)=12
We move all terms to the left:
4x(1/2x+6)-(12)=0
Domain of the equation: 2x+6)!=0We multiply parentheses
x∈R
4x^2+24x-12=0
a = 4; b = 24; c = -12;
Δ = b2-4ac
Δ = 242-4·4·(-12)
Δ = 768
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-16\sqrt{3}}{2*4}=\frac{-24-16\sqrt{3}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+16\sqrt{3}}{2*4}=\frac{-24+16\sqrt{3}}{8} $
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