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11-x(12x+5)-x=22x+2
We move all terms to the left:
11-x(12x+5)-x-(22x+2)=0
We add all the numbers together, and all the variables
-1x-x(12x+5)-(22x+2)+11=0
We multiply parentheses
-12x^2-1x-5x-(22x+2)+11=0
We get rid of parentheses
-12x^2-1x-5x-22x-2+11=0
We add all the numbers together, and all the variables
-12x^2-28x+9=0
a = -12; b = -28; c = +9;
Δ = b2-4ac
Δ = -282-4·(-12)·9
Δ = 1216
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-8\sqrt{19}}{2*-12}=\frac{28-8\sqrt{19}}{-24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+8\sqrt{19}}{2*-12}=\frac{28+8\sqrt{19}}{-24} $
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