25c^2+10=125-5c

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Solution for 25c^2+10=125-5c equation:



25c^2+10=125-5c
We move all terms to the left:
25c^2+10-(125-5c)=0
We add all the numbers together, and all the variables
25c^2-(-5c+125)+10=0
We get rid of parentheses
25c^2+5c-125+10=0
We add all the numbers together, and all the variables
25c^2+5c-115=0
a = 25; b = 5; c = -115;
Δ = b2-4ac
Δ = 52-4·25·(-115)
Δ = 11525
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:
$\sqrt{\Delta}=\sqrt{11525}=\sqrt{25*461}=\sqrt{25}*\sqrt{461}=5\sqrt{461}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{461}}{2*25}=\frac{-5-5\sqrt{461}}{50} $
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{461}}{2*25}=\frac{-5+5\sqrt{461}}{50} $

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