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2x(3x+7)=21
We move all terms to the left:
2x(3x+7)-(21)=0
We multiply parentheses
6x^2+14x-21=0
a = 6; b = 14; c = -21;
Δ = b2-4ac
Δ = 142-4·6·(-21)
Δ = 700
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-10\sqrt{7}}{2*6}=\frac{-14-10\sqrt{7}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+10\sqrt{7}}{2*6}=\frac{-14+10\sqrt{7}}{12} $
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