x*(x-1)=72

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Solution for x*(x-1)=72 equation:



x(x-1)=72
We move all terms to the left:
x(x-1)-(72)=0
We multiply parentheses
x^2-1x-72=0
a = 1; b = -1; c = -72;
Δ = b2-4ac
Δ = -12-4·1·(-72)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-17}{2*1}=\frac{-16}{2} =-8 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+17}{2*1}=\frac{18}{2} =9 $

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