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x(2x+9)=12
We move all terms to the left:
x(2x+9)-(12)=0
We multiply parentheses
2x^2+9x-12=0
a = 2; b = 9; c = -12;
Δ = b2-4ac
Δ = 92-4·2·(-12)
Δ = 177
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{-(9)-\sqrt{177}}{2*2}=\frac{-9-\sqrt{177}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{177}}{2*2}=\frac{-9+\sqrt{177}}{4} $
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