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3x(x-2)=x+4
We move all terms to the left:
3x(x-2)-(x+4)=0
We multiply parentheses
3x^2-6x-(x+4)=0
We get rid of parentheses
3x^2-6x-x-4=0
We add all the numbers together, and all the variables
3x^2-7x-4=0
a = 3; b = -7; c = -4;
Δ = b2-4ac
Δ = -72-4·3·(-4)
Δ = 97
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{97}}{2*3}=\frac{7-\sqrt{97}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{97}}{2*3}=\frac{7+\sqrt{97}}{6} $
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