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3x(x-1)-4=8
We move all terms to the left:
3x(x-1)-4-(8)=0
We add all the numbers together, and all the variables
3x(x-1)-12=0
We multiply parentheses
3x^2-3x-12=0
a = 3; b = -3; c = -12;
Δ = b2-4ac
Δ = -32-4·3·(-12)
Δ = 153
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{17}}{2*3}=\frac{3-3\sqrt{17}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{17}}{2*3}=\frac{3+3\sqrt{17}}{6} $
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