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x(30-x)=6x+44
We move all terms to the left:
x(30-x)-(6x+44)=0
We add all the numbers together, and all the variables
x(-1x+30)-(6x+44)=0
We multiply parentheses
-1x^2+30x-(6x+44)=0
We get rid of parentheses
-1x^2+30x-6x-44=0
We add all the numbers together, and all the variables
-1x^2+24x-44=0
a = -1; b = 24; c = -44;
Δ = b2-4ac
Δ = 242-4·(-1)·(-44)
Δ = 400
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{400}=20$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-20}{2*-1}=\frac{-44}{-2} =+22 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+20}{2*-1}=\frac{-4}{-2} =+2 $
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