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(4x)(x)(x+6)=102
We move all terms to the left:
(4x)(x)(x+6)-(102)=0
We multiply parentheses
4x^2+24x-102=0
a = 4; b = 24; c = -102;
Δ = b2-4ac
Δ = 242-4·4·(-102)
Δ = 2208
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2208}=\sqrt{16*138}=\sqrt{16}*\sqrt{138}=4\sqrt{138}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{138}}{2*4}=\frac{-24-4\sqrt{138}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{138}}{2*4}=\frac{-24+4\sqrt{138}}{8} $
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