6x^2-18=4x+2

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Solution for 6x^2-18=4x+2 equation:



6x^2-18=4x+2
We move all terms to the left:
6x^2-18-(4x+2)=0
We get rid of parentheses
6x^2-4x-2-18=0
We add all the numbers together, and all the variables
6x^2-4x-20=0
a = 6; b = -4; c = -20;
Δ = b2-4ac
Δ = -42-4·6·(-20)
Δ = 496
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:
$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{31}}{2*6}=\frac{4-4\sqrt{31}}{12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{31}}{2*6}=\frac{4+4\sqrt{31}}{12} $

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