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120x-x^2=120-2x
We move all terms to the left:
120x-x^2-(120-2x)=0
We add all the numbers together, and all the variables
-x^2+120x-(-2x+120)=0
We add all the numbers together, and all the variables
-1x^2+120x-(-2x+120)=0
We get rid of parentheses
-1x^2+120x+2x-120=0
We add all the numbers together, and all the variables
-1x^2+122x-120=0
a = -1; b = 122; c = -120;
Δ = b2-4ac
Δ = 1222-4·(-1)·(-120)
Δ = 14404
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{14404}=\sqrt{4*3601}=\sqrt{4}*\sqrt{3601}=2\sqrt{3601}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(122)-2\sqrt{3601}}{2*-1}=\frac{-122-2\sqrt{3601}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(122)+2\sqrt{3601}}{2*-1}=\frac{-122+2\sqrt{3601}}{-2} $
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