c^2+3c^2-81c-243=0

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Solution for c^2+3c^2-81c-243=0 equation:



c^2+3c^2-81c-243=0
We add all the numbers together, and all the variables
4c^2-81c-243=0
a = 4; b = -81; c = -243;
Δ = b2-4ac
Δ = -812-4·4·(-243)
Δ = 10449
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:
$\sqrt{\Delta}=\sqrt{10449}=\sqrt{81*129}=\sqrt{81}*\sqrt{129}=9\sqrt{129}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-9\sqrt{129}}{2*4}=\frac{81-9\sqrt{129}}{8} $
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+9\sqrt{129}}{2*4}=\frac{81+9\sqrt{129}}{8} $

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