x(x-30)=180

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Solution for x(x-30)=180 equation:



x(x-30)=180
We move all terms to the left:
x(x-30)-(180)=0
We multiply parentheses
x^2-30x-180=0
a = 1; b = -30; c = -180;
Δ = b2-4ac
Δ = -302-4·1·(-180)
Δ = 1620
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:
$\sqrt{\Delta}=\sqrt{1620}=\sqrt{324*5}=\sqrt{324}*\sqrt{5}=18\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-18\sqrt{5}}{2*1}=\frac{30-18\sqrt{5}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+18\sqrt{5}}{2*1}=\frac{30+18\sqrt{5}}{2} $

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