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4x(x-3)=x+9
We move all terms to the left:
4x(x-3)-(x+9)=0
We multiply parentheses
4x^2-12x-(x+9)=0
We get rid of parentheses
4x^2-12x-x-9=0
We add all the numbers together, and all the variables
4x^2-13x-9=0
a = 4; b = -13; c = -9;
Δ = b2-4ac
Δ = -132-4·4·(-9)
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*4}=\frac{13-\sqrt{313}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{313}}{2*4}=\frac{13+\sqrt{313}}{8} $
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