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x=-0.4x^2+1.74x+0
We move all terms to the left:
x-(-0.4x^2+1.74x+0)=0
We get rid of parentheses
0.4x^2-1.74x+x-0=0
We add all the numbers together, and all the variables
0.4x^2-0.74x=0
a = 0.4; b = -0.74; c = 0;
Δ = b2-4ac
Δ = -0.742-4·0.4·0
Δ = 0.5476
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{-(-0.74)-\sqrt{0.5476}}{2*0.4}=\frac{0.74-\sqrt{0.5476}}{0.8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.74)+\sqrt{0.5476}}{2*0.4}=\frac{0.74+\sqrt{0.5476}}{0.8} $
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