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2(x-3)4x=18
We move all terms to the left:
2(x-3)4x-(18)=0
We multiply parentheses
8x^2-24x-18=0
a = 8; b = -24; c = -18;
Δ = b2-4ac
Δ = -242-4·8·(-18)
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*8}=\frac{24-24\sqrt{2}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24\sqrt{2}}{2*8}=\frac{24+24\sqrt{2}}{16} $
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