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11(2x^2-3)-3=x
We move all terms to the left:
11(2x^2-3)-3-(x)=0
We add all the numbers together, and all the variables
-1x+11(2x^2-3)-3=0
We multiply parentheses
22x^2-1x-33-3=0
We add all the numbers together, and all the variables
22x^2-1x-36=0
a = 22; b = -1; c = -36;
Δ = b2-4ac
Δ = -12-4·22·(-36)
Δ = 3169
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{-(-1)-\sqrt{3169}}{2*22}=\frac{1-\sqrt{3169}}{44} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{3169}}{2*22}=\frac{1+\sqrt{3169}}{44} $
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