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0=-12x^2+1400x-38400
We move all terms to the left:
0-(-12x^2+1400x-38400)=0
We add all the numbers together, and all the variables
-(-12x^2+1400x-38400)=0
We get rid of parentheses
12x^2-1400x+38400=0
a = 12; b = -1400; c = +38400;
Δ = b2-4ac
Δ = -14002-4·12·38400
Δ = 116800
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{116800}=\sqrt{1600*73}=\sqrt{1600}*\sqrt{73}=40\sqrt{73}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1400)-40\sqrt{73}}{2*12}=\frac{1400-40\sqrt{73}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1400)+40\sqrt{73}}{2*12}=\frac{1400+40\sqrt{73}}{24} $
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