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7x(x+3)=21
We move all terms to the left:
7x(x+3)-(21)=0
We multiply parentheses
7x^2+21x-21=0
a = 7; b = 21; c = -21;
Δ = b2-4ac
Δ = 212-4·7·(-21)
Δ = 1029
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1029}=\sqrt{49*21}=\sqrt{49}*\sqrt{21}=7\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-7\sqrt{21}}{2*7}=\frac{-21-7\sqrt{21}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+7\sqrt{21}}{2*7}=\frac{-21+7\sqrt{21}}{14} $
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