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10x^2-6x=18
We move all terms to the left:
10x^2-6x-(18)=0
a = 10; b = -6; c = -18;
Δ = b2-4ac
Δ = -62-4·10·(-18)
Δ = 756
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{21}}{2*10}=\frac{6-6\sqrt{21}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{21}}{2*10}=\frac{6+6\sqrt{21}}{20} $
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