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9=-12.9+-8.6x+4.3x^2
We move all terms to the left:
9-(-12.9+-8.6x+4.3x^2)=0
We use the square of the difference formula
-(-12.9-8.6x+4.3x^2)+9=0
We get rid of parentheses
-4.3x^2+8.6x+12.9+9=0
We add all the numbers together, and all the variables
-4.3x^2+8.6x+21.9=0
a = -4.3; b = 8.6; c = +21.9;
Δ = b2-4ac
Δ = 8.62-4·(-4.3)·21.9
Δ = 450.64
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{-(8.6)-\sqrt{450.64}}{2*-4.3}=\frac{-8.6-\sqrt{450.64}}{-8.6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8.6)+\sqrt{450.64}}{2*-4.3}=\frac{-8.6+\sqrt{450.64}}{-8.6} $
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