12(2c+7)=c^2+17c+7

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Solution for 12(2c+7)=c^2+17c+7 equation:



12(2c+7)=c^2+17c+7
We move all terms to the left:
12(2c+7)-(c^2+17c+7)=0
We multiply parentheses
24c-(c^2+17c+7)+84=0
We get rid of parentheses
-c^2+24c-17c-7+84=0
We add all the numbers together, and all the variables
-1c^2+7c+77=0
a = -1; b = 7; c = +77;
Δ = b2-4ac
Δ = 72-4·(-1)·77
Δ = 357
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{357}}{2*-1}=\frac{-7-\sqrt{357}}{-2} $
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{357}}{2*-1}=\frac{-7+\sqrt{357}}{-2} $

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