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9=3x^2+4x-6
We move all terms to the left:
9-(3x^2+4x-6)=0
We get rid of parentheses
-3x^2-4x+6+9=0
We add all the numbers together, and all the variables
-3x^2-4x+15=0
a = -3; b = -4; c = +15;
Δ = b2-4ac
Δ = -42-4·(-3)·15
Δ = 196
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{196}=14$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-14}{2*-3}=\frac{-10}{-6} =1+2/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+14}{2*-3}=\frac{18}{-6} =-3 $
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