x2+8x=4

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Solution for x2+8x=4 equation:



x2+8x=4
We move all terms to the left:
x2+8x-(4)=0
We add all the numbers together, and all the variables
x^2+8x-4=0
a = 1; b = 8; c = -4;
Δ = b2-4ac
Δ = 82-4·1·(-4)
Δ = 80
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:
$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{5}}{2*1}=\frac{-8-4\sqrt{5}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{5}}{2*1}=\frac{-8+4\sqrt{5}}{2} $

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