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x(7x-1)-2(7x-1)=2
We move all terms to the left:
x(7x-1)-2(7x-1)-(2)=0
We multiply parentheses
7x^2-1x-14x+2-2=0
We add all the numbers together, and all the variables
7x^2-15x=0
a = 7; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·7·0
Δ = 225
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{225}=15$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*7}=\frac{0}{14} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*7}=\frac{30}{14} =2+1/7 $
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