x(x+52)=264

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Solution for x(x+52)=264 equation:



x(x+52)=264
We move all terms to the left:
x(x+52)-(264)=0
We multiply parentheses
x^2+52x-264=0
a = 1; b = 52; c = -264;
Δ = b2-4ac
Δ = 522-4·1·(-264)
Δ = 3760
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:
$\sqrt{\Delta}=\sqrt{3760}=\sqrt{16*235}=\sqrt{16}*\sqrt{235}=4\sqrt{235}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-4\sqrt{235}}{2*1}=\frac{-52-4\sqrt{235}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+4\sqrt{235}}{2*1}=\frac{-52+4\sqrt{235}}{2} $

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