X^2+3x=1+12x

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Solution for X^2+3x=1+12x equation:



X^2+3X=1+12X
We move all terms to the left:
X^2+3X-(1+12X)=0
We add all the numbers together, and all the variables
X^2+3X-(12X+1)=0
We get rid of parentheses
X^2+3X-12X-1=0
We add all the numbers together, and all the variables
X^2-9X-1=0
a = 1; b = -9; c = -1;
Δ = b2-4ac
Δ = -92-4·1·(-1)
Δ = 85
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{-(-9)-\sqrt{85}}{2*1}=\frac{9-\sqrt{85}}{2} $
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{85}}{2*1}=\frac{9+\sqrt{85}}{2} $

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