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9x-3=-x^2-9x
We move all terms to the left:
9x-3-(-x^2-9x)=0
We get rid of parentheses
x^2+9x+9x-3=0
We add all the numbers together, and all the variables
x^2+18x-3=0
a = 1; b = 18; c = -3;
Δ = b2-4ac
Δ = 182-4·1·(-3)
Δ = 336
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-4\sqrt{21}}{2*1}=\frac{-18-4\sqrt{21}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+4\sqrt{21}}{2*1}=\frac{-18+4\sqrt{21}}{2} $
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