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(3x-2)(7x-2)=x
We move all terms to the left:
(3x-2)(7x-2)-(x)=0
We add all the numbers together, and all the variables
-1x+(3x-2)(7x-2)=0
We multiply parentheses ..
(+21x^2-6x-14x+4)-1x=0
We get rid of parentheses
21x^2-6x-14x-1x+4=0
We add all the numbers together, and all the variables
21x^2-21x+4=0
a = 21; b = -21; c = +4;
Δ = b2-4ac
Δ = -212-4·21·4
Δ = 105
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{-(-21)-\sqrt{105}}{2*21}=\frac{21-\sqrt{105}}{42} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{105}}{2*21}=\frac{21+\sqrt{105}}{42} $
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