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2x(x-18)=180
We move all terms to the left:
2x(x-18)-(180)=0
We multiply parentheses
2x^2-36x-180=0
a = 2; b = -36; c = -180;
Δ = b2-4ac
Δ = -362-4·2·(-180)
Δ = 2736
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2736}=\sqrt{144*19}=\sqrt{144}*\sqrt{19}=12\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{19}}{2*2}=\frac{36-12\sqrt{19}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{19}}{2*2}=\frac{36+12\sqrt{19}}{4} $
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