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x(x-24)=180
We move all terms to the left:
x(x-24)-(180)=0
We multiply parentheses
x^2-24x-180=0
a = 1; b = -24; c = -180;
Δ = b2-4ac
Δ = -242-4·1·(-180)
Δ = 1296
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{1296}=36$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-36}{2*1}=\frac{-12}{2} =-6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+36}{2*1}=\frac{60}{2} =30 $
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