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-4x^2+1=9x
We move all terms to the left:
-4x^2+1-(9x)=0
a = -4; b = -9; c = +1;
Δ = b2-4ac
Δ = -92-4·(-4)·1
Δ = 97
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{97}}{2*-4}=\frac{9-\sqrt{97}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{97}}{2*-4}=\frac{9+\sqrt{97}}{-8} $
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