25x-(5-x)(5+x)=0

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Solution for 25x-(5-x)(5+x)=0 equation:



25x-(5-x)(5+x)=0
We add all the numbers together, and all the variables
25x-(-1x+5)(x+5)=0
We multiply parentheses ..
-(-1x^2-5x+5x+25)+25x=0
We get rid of parentheses
1x^2+5x-5x+25x-25=0
We add all the numbers together, and all the variables
x^2+25x-25=0
a = 1; b = 25; c = -25;
Δ = b2-4ac
Δ = 252-4·1·(-25)
Δ = 725
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:
$\sqrt{\Delta}=\sqrt{725}=\sqrt{25*29}=\sqrt{25}*\sqrt{29}=5\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-5\sqrt{29}}{2*1}=\frac{-25-5\sqrt{29}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+5\sqrt{29}}{2*1}=\frac{-25+5\sqrt{29}}{2} $

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