(x-5)(x+5)=-20

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Solution for (x-5)(x+5)=-20 equation:



(x-5)(x+5)=-20
We move all terms to the left:
(x-5)(x+5)-(-20)=0
We add all the numbers together, and all the variables
(x-5)(x+5)+20=0
We use the square of the difference formula
x^2-25+20=0
We add all the numbers together, and all the variables
x^2-5=0
a = 1; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·1·(-5)
Δ = 20
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:
$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{5}}{2*1}=\frac{0-2\sqrt{5}}{2} =-\frac{2\sqrt{5}}{2} =-\sqrt{5} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{5}}{2*1}=\frac{0+2\sqrt{5}}{2} =\frac{2\sqrt{5}}{2} =\sqrt{5} $

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