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2x(3x+2)-9=3x-10+5
We move all terms to the left:
2x(3x+2)-9-(3x-10+5)=0
We add all the numbers together, and all the variables
2x(3x+2)-(3x-5)-9=0
We multiply parentheses
6x^2+4x-(3x-5)-9=0
We get rid of parentheses
6x^2+4x-3x+5-9=0
We add all the numbers together, and all the variables
6x^2+x-4=0
a = 6; b = 1; c = -4;
Δ = b2-4ac
Δ = 12-4·6·(-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{-(1)-\sqrt{97}}{2*6}=\frac{-1-\sqrt{97}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{97}}{2*6}=\frac{-1+\sqrt{97}}{12} $
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