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5.6x(x-3)=0.4x+19.2
We move all terms to the left:
5.6x(x-3)-(0.4x+19.2)=0
We multiply parentheses
5x^2-15x-(0.4x+19.2)=0
We get rid of parentheses
5x^2-15x-0.4x-19.2=0
We add all the numbers together, and all the variables
5x^2-15.4x-19.2=0
a = 5; b = -15.4; c = -19.2;
Δ = b2-4ac
Δ = -15.42-4·5·(-19.2)
Δ = 621.16
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{-(-15.4)-\sqrt{621.16}}{2*5}=\frac{15.4-\sqrt{621.16}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15.4)+\sqrt{621.16}}{2*5}=\frac{15.4+\sqrt{621.16}}{10} $
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