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11-4x(3x-1)-5(4x-3)=3x
We move all terms to the left:
11-4x(3x-1)-5(4x-3)-(3x)=0
We add all the numbers together, and all the variables
-3x-4x(3x-1)-5(4x-3)+11=0
We multiply parentheses
-12x^2-3x+4x-20x+15+11=0
We add all the numbers together, and all the variables
-12x^2-19x+26=0
a = -12; b = -19; c = +26;
Δ = b2-4ac
Δ = -192-4·(-12)·26
Δ = 1609
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{-(-19)-\sqrt{1609}}{2*-12}=\frac{19-\sqrt{1609}}{-24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{1609}}{2*-12}=\frac{19+\sqrt{1609}}{-24} $
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