X(x-28)=124

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Solution for X(x-28)=124 equation:



X(X-28)=124
We move all terms to the left:
X(X-28)-(124)=0
We multiply parentheses
X^2-28X-124=0
a = 1; b = -28; c = -124;
Δ = b2-4ac
Δ = -282-4·1·(-124)
Δ = 1280
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:
$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-16\sqrt{5}}{2*1}=\frac{28-16\sqrt{5}}{2} $
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+16\sqrt{5}}{2*1}=\frac{28+16\sqrt{5}}{2} $

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