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-x^2-9=-30
We move all terms to the left:
-x^2-9-(-30)=0
We add all the numbers together, and all the variables
-1x^2+21=0
a = -1; b = 0; c = +21;
Δ = b2-4ac
Δ = 02-4·(-1)·21
Δ = 84
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{21}}{2*-1}=\frac{0-2\sqrt{21}}{-2} =-\frac{2\sqrt{21}}{-2} =-\frac{\sqrt{21}}{-1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{21}}{2*-1}=\frac{0+2\sqrt{21}}{-2} =\frac{2\sqrt{21}}{-2} =\frac{\sqrt{21}}{-1} $
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