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(20k+4)(33k-9)=360
We move all terms to the left:
(20k+4)(33k-9)-(360)=0
We multiply parentheses ..
(+660k^2-180k+132k-36)-360=0
We get rid of parentheses
660k^2-180k+132k-36-360=0
We add all the numbers together, and all the variables
660k^2-48k-396=0
a = 660; b = -48; c = -396;
Δ = b2-4ac
Δ = -482-4·660·(-396)
Δ = 1047744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1047744}=\sqrt{576*1819}=\sqrt{576}*\sqrt{1819}=24\sqrt{1819}$$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-24\sqrt{1819}}{2*660}=\frac{48-24\sqrt{1819}}{1320} $$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+24\sqrt{1819}}{2*660}=\frac{48+24\sqrt{1819}}{1320} $
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