6x2=x+1

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Solution for 6x2=x+1 equation:



6x^2=x+1
We move all terms to the left:
6x^2-(x+1)=0
We get rid of parentheses
6x^2-x-1=0
We add all the numbers together, and all the variables
6x^2-1x-1=0
a = 6; b = -1; c = -1;
Δ = b2-4ac
Δ = -12-4·6·(-1)
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{-(-1)-5}{2*6}=\frac{-4}{12} =-1/3 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5}{2*6}=\frac{6}{12} =1/2 $

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