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12x(3x-4)=14-7
We move all terms to the left:
12x(3x-4)-(14-7)=0
We add all the numbers together, and all the variables
12x(3x-4)-7=0
We multiply parentheses
36x^2-48x-7=0
a = 36; b = -48; c = -7;
Δ = b2-4ac
Δ = -482-4·36·(-7)
Δ = 3312
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3312}=\sqrt{144*23}=\sqrt{144}*\sqrt{23}=12\sqrt{23}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-12\sqrt{23}}{2*36}=\frac{48-12\sqrt{23}}{72} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+12\sqrt{23}}{2*36}=\frac{48+12\sqrt{23}}{72} $
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