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x(2x-9)=-8
We move all terms to the left:
x(2x-9)-(-8)=0
We add all the numbers together, and all the variables
x(2x-9)+8=0
We multiply parentheses
2x^2-9x+8=0
a = 2; b = -9; c = +8;
Δ = b2-4ac
Δ = -92-4·2·8
Δ = 17
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{17}}{2*2}=\frac{9-\sqrt{17}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{17}}{2*2}=\frac{9+\sqrt{17}}{4} $
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