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2x(-4x+1)=3x-1
We move all terms to the left:
2x(-4x+1)-(3x-1)=0
We multiply parentheses
-8x^2+2x-(3x-1)=0
We get rid of parentheses
-8x^2+2x-3x+1=0
We add all the numbers together, and all the variables
-8x^2-1x+1=0
a = -8; b = -1; c = +1;
Δ = b2-4ac
Δ = -12-4·(-8)·1
Δ = 33
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{-(-1)-\sqrt{33}}{2*-8}=\frac{1-\sqrt{33}}{-16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{33}}{2*-8}=\frac{1+\sqrt{33}}{-16} $
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