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6x(x-1)=9-31x
We move all terms to the left:
6x(x-1)-(9-31x)=0
We add all the numbers together, and all the variables
6x(x-1)-(-31x+9)=0
We multiply parentheses
6x^2-6x-(-31x+9)=0
We get rid of parentheses
6x^2-6x+31x-9=0
We add all the numbers together, and all the variables
6x^2+25x-9=0
a = 6; b = 25; c = -9;
Δ = b2-4ac
Δ = 252-4·6·(-9)
Δ = 841
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{841}=29$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-29}{2*6}=\frac{-54}{12} =-4+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+29}{2*6}=\frac{4}{12} =1/3 $
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