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2x(3x+1)=9
We move all terms to the left:
2x(3x+1)-(9)=0
We multiply parentheses
6x^2+2x-9=0
a = 6; b = 2; c = -9;
Δ = b2-4ac
Δ = 22-4·6·(-9)
Δ = 220
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{55}}{2*6}=\frac{-2-2\sqrt{55}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{55}}{2*6}=\frac{-2+2\sqrt{55}}{12} $
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