x2+x=380

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Solution for x2+x=380 equation:



x2+x=380
We move all terms to the left:
x2+x-(380)=0
We add all the numbers together, and all the variables
x^2+x-380=0
a = 1; b = 1; c = -380;
Δ = b2-4ac
Δ = 12-4·1·(-380)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-39}{2*1}=\frac{-40}{2} =-20 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+39}{2*1}=\frac{38}{2} =19 $

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