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3-7x^2+9=x
We move all terms to the left:
3-7x^2+9-(x)=0
We add all the numbers together, and all the variables
-7x^2-1x+12=0
a = -7; b = -1; c = +12;
Δ = b2-4ac
Δ = -12-4·(-7)·12
Δ = 337
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{337}}{2*-7}=\frac{1-\sqrt{337}}{-14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{337}}{2*-7}=\frac{1+\sqrt{337}}{-14} $
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