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X(X+6)=84
We move all terms to the left:
X(X+6)-(84)=0
We multiply parentheses
X^2+6X-84=0
a = 1; b = 6; c = -84;
Δ = b2-4ac
Δ = 62-4·1·(-84)
Δ = 372
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{93}}{2*1}=\frac{-6-2\sqrt{93}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{93}}{2*1}=\frac{-6+2\sqrt{93}}{2} $
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