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2x(x-3)+3(x-2)=18
We move all terms to the left:
2x(x-3)+3(x-2)-(18)=0
We multiply parentheses
2x^2-6x+3x-6-18=0
We add all the numbers together, and all the variables
2x^2-3x-24=0
a = 2; b = -3; c = -24;
Δ = b2-4ac
Δ = -32-4·2·(-24)
Δ = 201
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{-(-3)-\sqrt{201}}{2*2}=\frac{3-\sqrt{201}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{201}}{2*2}=\frac{3+\sqrt{201}}{4} $
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