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3(x-2)5x=18
We move all terms to the left:
3(x-2)5x-(18)=0
We multiply parentheses
15x^2-30x-18=0
a = 15; b = -30; c = -18;
Δ = b2-4ac
Δ = -302-4·15·(-18)
Δ = 1980
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1980}=\sqrt{36*55}=\sqrt{36}*\sqrt{55}=6\sqrt{55}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{55}}{2*15}=\frac{30-6\sqrt{55}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{55}}{2*15}=\frac{30+6\sqrt{55}}{30} $
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