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12c(4c-1)-12=46c+12
We move all terms to the left:
12c(4c-1)-12-(46c+12)=0
We multiply parentheses
48c^2-12c-(46c+12)-12=0
We get rid of parentheses
48c^2-12c-46c-12-12=0
We add all the numbers together, and all the variables
48c^2-58c-24=0
a = 48; b = -58; c = -24;
Δ = b2-4ac
Δ = -582-4·48·(-24)
Δ = 7972
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7972}=\sqrt{4*1993}=\sqrt{4}*\sqrt{1993}=2\sqrt{1993}$$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-2\sqrt{1993}}{2*48}=\frac{58-2\sqrt{1993}}{96} $$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+2\sqrt{1993}}{2*48}=\frac{58+2\sqrt{1993}}{96} $
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