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0=-400x^2+400x-90
We move all terms to the left:
0-(-400x^2+400x-90)=0
We add all the numbers together, and all the variables
-(-400x^2+400x-90)=0
We get rid of parentheses
400x^2-400x+90=0
a = 400; b = -400; c = +90;
Δ = b2-4ac
Δ = -4002-4·400·90
Δ = 16000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{16000}=\sqrt{1600*10}=\sqrt{1600}*\sqrt{10}=40\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-40\sqrt{10}}{2*400}=\frac{400-40\sqrt{10}}{800} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+40\sqrt{10}}{2*400}=\frac{400+40\sqrt{10}}{800} $
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