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6-2x(x-9)=x+9
We move all terms to the left:
6-2x(x-9)-(x+9)=0
We multiply parentheses
-2x^2+18x-(x+9)+6=0
We get rid of parentheses
-2x^2+18x-x-9+6=0
We add all the numbers together, and all the variables
-2x^2+17x-3=0
a = -2; b = 17; c = -3;
Δ = b2-4ac
Δ = 172-4·(-2)·(-3)
Δ = 265
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{-(17)-\sqrt{265}}{2*-2}=\frac{-17-\sqrt{265}}{-4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{265}}{2*-2}=\frac{-17+\sqrt{265}}{-4} $
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