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0.1x^2+2.4x+25=500
We move all terms to the left:
0.1x^2+2.4x+25-(500)=0
We add all the numbers together, and all the variables
0.1x^2+2.4x-475=0
a = 0.1; b = 2.4; c = -475;
Δ = b2-4ac
Δ = 2.42-4·0.1·(-475)
Δ = 195.76
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{-(2.4)-\sqrt{195.76}}{2*0.1}=\frac{-2.4-\sqrt{195.76}}{0.2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.4)+\sqrt{195.76}}{2*0.1}=\frac{-2.4+\sqrt{195.76}}{0.2} $
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