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600-50x=2x*x
We move all terms to the left:
600-50x-(2x*x)=0
We add all the numbers together, and all the variables
-50x-(+2x*x)+600=0
We get rid of parentheses
-50x-2x*x+600=0
Wy multiply elements
-2x^2-50x+600=0
a = -2; b = -50; c = +600;
Δ = b2-4ac
Δ = -502-4·(-2)·600
Δ = 7300
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7300}=\sqrt{100*73}=\sqrt{100}*\sqrt{73}=10\sqrt{73}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{73}}{2*-2}=\frac{50-10\sqrt{73}}{-4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{73}}{2*-2}=\frac{50+10\sqrt{73}}{-4} $
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