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350=-0.4x^2+280x-24000
We move all terms to the left:
350-(-0.4x^2+280x-24000)=0
We get rid of parentheses
0.4x^2-280x+24000+350=0
We add all the numbers together, and all the variables
0.4x^2-280x+24350=0
a = 0.4; b = -280; c = +24350;
Δ = b2-4ac
Δ = -2802-4·0.4·24350
Δ = 39440
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{39440}=\sqrt{16*2465}=\sqrt{16}*\sqrt{2465}=4\sqrt{2465}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-280)-4\sqrt{2465}}{2*0.4}=\frac{280-4\sqrt{2465}}{0.8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-280)+4\sqrt{2465}}{2*0.4}=\frac{280+4\sqrt{2465}}{0.8} $
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