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9x^2-8x+2=15
We move all terms to the left:
9x^2-8x+2-(15)=0
We add all the numbers together, and all the variables
9x^2-8x-13=0
a = 9; b = -8; c = -13;
Δ = b2-4ac
Δ = -82-4·9·(-13)
Δ = 532
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{532}=\sqrt{4*133}=\sqrt{4}*\sqrt{133}=2\sqrt{133}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{133}}{2*9}=\frac{8-2\sqrt{133}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{133}}{2*9}=\frac{8+2\sqrt{133}}{18} $
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