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400x+5x^2=1200
We move all terms to the left:
400x+5x^2-(1200)=0
a = 5; b = 400; c = -1200;
Δ = b2-4ac
Δ = 4002-4·5·(-1200)
Δ = 184000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{184000}=\sqrt{1600*115}=\sqrt{1600}*\sqrt{115}=40\sqrt{115}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-40\sqrt{115}}{2*5}=\frac{-400-40\sqrt{115}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+40\sqrt{115}}{2*5}=\frac{-400+40\sqrt{115}}{10} $
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