(X-1)(x+1)+5x-3=0

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Solution for (X-1)(x+1)+5x-3=0 equation:



(X-1)(X+1)+5X-3=0
We add all the numbers together, and all the variables
5X+(X-1)(X+1)-3=0
We use the square of the difference formula
X^2+5X-1-3=0
We add all the numbers together, and all the variables
X^2+5X-4=0
a = 1; b = 5; c = -4;
Δ = b2-4ac
Δ = 52-4·1·(-4)
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{41}}{2*1}=\frac{-5-\sqrt{41}}{2} $
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{41}}{2*1}=\frac{-5+\sqrt{41}}{2} $

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