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7x^2=18x-9
We move all terms to the left:
7x^2-(18x-9)=0
We get rid of parentheses
7x^2-18x+9=0
a = 7; b = -18; c = +9;
Δ = b2-4ac
Δ = -182-4·7·9
Δ = 72
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{2}}{2*7}=\frac{18-6\sqrt{2}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{2}}{2*7}=\frac{18+6\sqrt{2}}{14} $
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