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(4x-1)(3x-1)=54
We move all terms to the left:
(4x-1)(3x-1)-(54)=0
We multiply parentheses ..
(+12x^2-4x-3x+1)-54=0
We get rid of parentheses
12x^2-4x-3x+1-54=0
We add all the numbers together, and all the variables
12x^2-7x-53=0
a = 12; b = -7; c = -53;
Δ = b2-4ac
Δ = -72-4·12·(-53)
Δ = 2593
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{2593}}{2*12}=\frac{7-\sqrt{2593}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{2593}}{2*12}=\frac{7+\sqrt{2593}}{24} $
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