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-x2+9x+5=-3
We move all terms to the left:
-x2+9x+5-(-3)=0
We add all the numbers together, and all the variables
-1x^2+9x+8=0
a = -1; b = 9; c = +8;
Δ = b2-4ac
Δ = 92-4·(-1)·8
Δ = 113
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{113}}{2*-1}=\frac{-9-\sqrt{113}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{113}}{2*-1}=\frac{-9+\sqrt{113}}{-2} $
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