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x(x+14)=208
We move all terms to the left:
x(x+14)-(208)=0
We multiply parentheses
x^2+14x-208=0
a = 1; b = 14; c = -208;
Δ = b2-4ac
Δ = 142-4·1·(-208)
Δ = 1028
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1028}=\sqrt{4*257}=\sqrt{4}*\sqrt{257}=2\sqrt{257}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{257}}{2*1}=\frac{-14-2\sqrt{257}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{257}}{2*1}=\frac{-14+2\sqrt{257}}{2} $
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