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3x^2+6x=1/3
We move all terms to the left:
3x^2+6x-(1/3)=0
We add all the numbers together, and all the variables
3x^2+6x-(+1/3)=0
We get rid of parentheses
3x^2+6x-1/3=0
We multiply all the terms by the denominator
3x^2*3+6x*3-1=0
Wy multiply elements
9x^2+18x-1=0
a = 9; b = 18; c = -1;
Δ = b2-4ac
Δ = 182-4·9·(-1)
Δ = 360
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{10}}{2*9}=\frac{-18-6\sqrt{10}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{10}}{2*9}=\frac{-18+6\sqrt{10}}{18} $
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