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0.5(4x-6)(x)=54
We move all terms to the left:
0.5(4x-6)(x)-(54)=0
We multiply parentheses
0x^2+0x-54=0
We add all the numbers together, and all the variables
x^2+x-54=0
a = 1; b = 1; c = -54;
Δ = b2-4ac
Δ = 12-4·1·(-54)
Δ = 217
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{217}}{2*1}=\frac{-1-\sqrt{217}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{217}}{2*1}=\frac{-1+\sqrt{217}}{2} $
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