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(3x-1)(3x-1)+1=14x-2
We move all terms to the left:
(3x-1)(3x-1)+1-(14x-2)=0
We get rid of parentheses
(3x-1)(3x-1)-14x+2+1=0
We multiply parentheses ..
(+9x^2-3x-3x+1)-14x+2+1=0
We add all the numbers together, and all the variables
(+9x^2-3x-3x+1)-14x+3=0
We get rid of parentheses
9x^2-3x-3x-14x+1+3=0
We add all the numbers together, and all the variables
9x^2-20x+4=0
a = 9; b = -20; c = +4;
Δ = b2-4ac
Δ = -202-4·9·4
Δ = 256
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{256}=16$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-16}{2*9}=\frac{4}{18} =2/9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+16}{2*9}=\frac{36}{18} =2 $
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