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(7x-1)(2x-1)=2x
We move all terms to the left:
(7x-1)(2x-1)-(2x)=0
We add all the numbers together, and all the variables
-2x+(7x-1)(2x-1)=0
We multiply parentheses ..
(+14x^2-7x-2x+1)-2x=0
We get rid of parentheses
14x^2-7x-2x-2x+1=0
We add all the numbers together, and all the variables
14x^2-11x+1=0
a = 14; b = -11; c = +1;
Δ = b2-4ac
Δ = -112-4·14·1
Δ = 65
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{-(-11)-\sqrt{65}}{2*14}=\frac{11-\sqrt{65}}{28} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{65}}{2*14}=\frac{11+\sqrt{65}}{28} $
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