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3x(x+4)=21
We move all terms to the left:
3x(x+4)-(21)=0
We multiply parentheses
3x^2+12x-21=0
a = 3; b = 12; c = -21;
Δ = b2-4ac
Δ = 122-4·3·(-21)
Δ = 396
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{11}}{2*3}=\frac{-12-6\sqrt{11}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{11}}{2*3}=\frac{-12+6\sqrt{11}}{6} $
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