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7x(x+7)=84
We move all terms to the left:
7x(x+7)-(84)=0
We multiply parentheses
7x^2+49x-84=0
a = 7; b = 49; c = -84;
Δ = b2-4ac
Δ = 492-4·7·(-84)
Δ = 4753
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4753}=\sqrt{49*97}=\sqrt{49}*\sqrt{97}=7\sqrt{97}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-7\sqrt{97}}{2*7}=\frac{-49-7\sqrt{97}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+7\sqrt{97}}{2*7}=\frac{-49+7\sqrt{97}}{14} $
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