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3x^2-6x+2=9-4x
We move all terms to the left:
3x^2-6x+2-(9-4x)=0
We add all the numbers together, and all the variables
3x^2-6x-(-4x+9)+2=0
We get rid of parentheses
3x^2-6x+4x-9+2=0
We add all the numbers together, and all the variables
3x^2-2x-7=0
a = 3; b = -2; c = -7;
Δ = b2-4ac
Δ = -22-4·3·(-7)
Δ = 88
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{22}}{2*3}=\frac{2-2\sqrt{22}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{22}}{2*3}=\frac{2+2\sqrt{22}}{6} $
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