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x*x-8x+9=56
We move all terms to the left:
x*x-8x+9-(56)=0
We add all the numbers together, and all the variables
-8x+x*x-47=0
Wy multiply elements
x^2-8x-47=0
a = 1; b = -8; c = -47;
Δ = b2-4ac
Δ = -82-4·1·(-47)
Δ = 252
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-6\sqrt{7}}{2*1}=\frac{8-6\sqrt{7}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6\sqrt{7}}{2*1}=\frac{8+6\sqrt{7}}{2} $
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