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4x(2x-6)=24
We move all terms to the left:
4x(2x-6)-(24)=0
We multiply parentheses
8x^2-24x-24=0
a = 8; b = -24; c = -24;
Δ = b2-4ac
Δ = -242-4·8·(-24)
Δ = 1344
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{21}}{2*8}=\frac{24-8\sqrt{21}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{21}}{2*8}=\frac{24+8\sqrt{21}}{16} $
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