6x2-22x+16=-2

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Solution for 6x2-22x+16=-2 equation:



6x^2-22x+16=-2
We move all terms to the left:
6x^2-22x+16-(-2)=0
We add all the numbers together, and all the variables
6x^2-22x+18=0
a = 6; b = -22; c = +18;
Δ = b2-4ac
Δ = -222-4·6·18
Δ = 52
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:
$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{13}}{2*6}=\frac{22-2\sqrt{13}}{12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{13}}{2*6}=\frac{22+2\sqrt{13}}{12} $

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