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4x(2x-1)-3x=11
We move all terms to the left:
4x(2x-1)-3x-(11)=0
We add all the numbers together, and all the variables
-3x+4x(2x-1)-11=0
We multiply parentheses
8x^2-3x-4x-11=0
We add all the numbers together, and all the variables
8x^2-7x-11=0
a = 8; b = -7; c = -11;
Δ = b2-4ac
Δ = -72-4·8·(-11)
Δ = 401
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{-(-7)-\sqrt{401}}{2*8}=\frac{7-\sqrt{401}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{401}}{2*8}=\frac{7+\sqrt{401}}{16} $
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