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3x(2x+8)=6x+18
We move all terms to the left:
3x(2x+8)-(6x+18)=0
We multiply parentheses
6x^2+24x-(6x+18)=0
We get rid of parentheses
6x^2+24x-6x-18=0
We add all the numbers together, and all the variables
6x^2+18x-18=0
a = 6; b = 18; c = -18;
Δ = b2-4ac
Δ = 182-4·6·(-18)
Δ = 756
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{21}}{2*6}=\frac{-18-6\sqrt{21}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{21}}{2*6}=\frac{-18+6\sqrt{21}}{12} $
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