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6x+3(-2x+4)x=-2
We move all terms to the left:
6x+3(-2x+4)x-(-2)=0
We add all the numbers together, and all the variables
6x+3(-2x+4)x+2=0
We multiply parentheses
-6x^2+6x+12x+2=0
We add all the numbers together, and all the variables
-6x^2+18x+2=0
a = -6; b = 18; c = +2;
Δ = b2-4ac
Δ = 182-4·(-6)·2
Δ = 372
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{93}}{2*-6}=\frac{-18-2\sqrt{93}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{93}}{2*-6}=\frac{-18+2\sqrt{93}}{-12} $
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