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4x(6x-32)=100x-12
We move all terms to the left:
4x(6x-32)-(100x-12)=0
We multiply parentheses
24x^2-128x-(100x-12)=0
We get rid of parentheses
24x^2-128x-100x+12=0
We add all the numbers together, and all the variables
24x^2-228x+12=0
a = 24; b = -228; c = +12;
Δ = b2-4ac
Δ = -2282-4·24·12
Δ = 50832
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{50832}=\sqrt{144*353}=\sqrt{144}*\sqrt{353}=12\sqrt{353}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-228)-12\sqrt{353}}{2*24}=\frac{228-12\sqrt{353}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-228)+12\sqrt{353}}{2*24}=\frac{228+12\sqrt{353}}{48} $
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