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x^2-17x+23=-5x-4
We move all terms to the left:
x^2-17x+23-(-5x-4)=0
We get rid of parentheses
x^2-17x+5x+4+23=0
We add all the numbers together, and all the variables
x^2-12x+27=0
a = 1; b = -12; c = +27;
Δ = b2-4ac
Δ = -122-4·1·27
Δ = 36
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{36}=6$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6}{2*1}=\frac{6}{2} =3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6}{2*1}=\frac{18}{2} =9 $
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