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6x-18=-4x^2
We move all terms to the left:
6x-18-(-4x^2)=0
We get rid of parentheses
4x^2+6x-18=0
a = 4; b = 6; c = -18;
Δ = b2-4ac
Δ = 62-4·4·(-18)
Δ = 324
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{324}=18$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-18}{2*4}=\frac{-24}{8} =-3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+18}{2*4}=\frac{12}{8} =1+1/2 $
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