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3x(2x+6)=82
We move all terms to the left:
3x(2x+6)-(82)=0
We multiply parentheses
6x^2+18x-82=0
a = 6; b = 18; c = -82;
Δ = b2-4ac
Δ = 182-4·6·(-82)
Δ = 2292
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2292}=\sqrt{4*573}=\sqrt{4}*\sqrt{573}=2\sqrt{573}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{573}}{2*6}=\frac{-18-2\sqrt{573}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{573}}{2*6}=\frac{-18+2\sqrt{573}}{12} $
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