5=x2+3x+1

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Solution for 5=x2+3x+1 equation:



5=x2+3x+1
We move all terms to the left:
5-(x2+3x+1)=0
We add all the numbers together, and all the variables
-(+x^2+3x+1)+5=0
We get rid of parentheses
-x^2-3x-1+5=0
We add all the numbers together, and all the variables
-1x^2-3x+4=0
a = -1; b = -3; c = +4;
Δ = b2-4ac
Δ = -32-4·(-1)·4
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-5}{2*-1}=\frac{-2}{-2} =1 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+5}{2*-1}=\frac{8}{-2} =-4 $

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