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3x(4x+9)=21
We move all terms to the left:
3x(4x+9)-(21)=0
We multiply parentheses
12x^2+27x-21=0
a = 12; b = 27; c = -21;
Δ = b2-4ac
Δ = 272-4·12·(-21)
Δ = 1737
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1737}=\sqrt{9*193}=\sqrt{9}*\sqrt{193}=3\sqrt{193}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{193}}{2*12}=\frac{-27-3\sqrt{193}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{193}}{2*12}=\frac{-27+3\sqrt{193}}{24} $
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