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3x(x-4)=2x+6
We move all terms to the left:
3x(x-4)-(2x+6)=0
We multiply parentheses
3x^2-12x-(2x+6)=0
We get rid of parentheses
3x^2-12x-2x-6=0
We add all the numbers together, and all the variables
3x^2-14x-6=0
a = 3; b = -14; c = -6;
Δ = b2-4ac
Δ = -142-4·3·(-6)
Δ = 268
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{67}}{2*3}=\frac{14-2\sqrt{67}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{67}}{2*3}=\frac{14+2\sqrt{67}}{6} $
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