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2(4x-12)3x=6x-1
We move all terms to the left:
2(4x-12)3x-(6x-1)=0
We multiply parentheses
24x^2-72x-(6x-1)=0
We get rid of parentheses
24x^2-72x-6x+1=0
We add all the numbers together, and all the variables
24x^2-78x+1=0
a = 24; b = -78; c = +1;
Δ = b2-4ac
Δ = -782-4·24·1
Δ = 5988
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5988}=\sqrt{4*1497}=\sqrt{4}*\sqrt{1497}=2\sqrt{1497}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{1497}}{2*24}=\frac{78-2\sqrt{1497}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{1497}}{2*24}=\frac{78+2\sqrt{1497}}{48} $
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