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3x(x-3)=4+2x
We move all terms to the left:
3x(x-3)-(4+2x)=0
We add all the numbers together, and all the variables
3x(x-3)-(2x+4)=0
We multiply parentheses
3x^2-9x-(2x+4)=0
We get rid of parentheses
3x^2-9x-2x-4=0
We add all the numbers together, and all the variables
3x^2-11x-4=0
a = 3; b = -11; c = -4;
Δ = b2-4ac
Δ = -112-4·3·(-4)
Δ = 169
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{169}=13$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-13}{2*3}=\frac{-2}{6} =-1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+13}{2*3}=\frac{24}{6} =4 $
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