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-2x(x-1)=-3x+1
We move all terms to the left:
-2x(x-1)-(-3x+1)=0
We multiply parentheses
-2x^2+2x-(-3x+1)=0
We get rid of parentheses
-2x^2+2x+3x-1=0
We add all the numbers together, and all the variables
-2x^2+5x-1=0
a = -2; b = 5; c = -1;
Δ = b2-4ac
Δ = 52-4·(-2)·(-1)
Δ = 17
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{-(5)-\sqrt{17}}{2*-2}=\frac{-5-\sqrt{17}}{-4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{17}}{2*-2}=\frac{-5+\sqrt{17}}{-4} $
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