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9x^2-12x+4=x+8
We move all terms to the left:
9x^2-12x+4-(x+8)=0
We get rid of parentheses
9x^2-12x-x-8+4=0
We add all the numbers together, and all the variables
9x^2-13x-4=0
a = 9; b = -13; c = -4;
Δ = b2-4ac
Δ = -132-4·9·(-4)
Δ = 313
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{-(-13)-\sqrt{313}}{2*9}=\frac{13-\sqrt{313}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{313}}{2*9}=\frac{13+\sqrt{313}}{18} $
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