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8650=x(114-0.055x)
We move all terms to the left:
8650-(x(114-0.055x))=0
We add all the numbers together, and all the variables
-(x(-0.055x+114))+8650=0
We calculate terms in parentheses: -(x(-0.055x+114)), so:We get rid of parentheses
x(-0.055x+114)
We multiply parentheses
0x^2+114x
We add all the numbers together, and all the variables
x^2+114x
Back to the equation:
-(x^2+114x)
-x^2-114x+8650=0
We add all the numbers together, and all the variables
-1x^2-114x+8650=0
a = -1; b = -114; c = +8650;
Δ = b2-4ac
Δ = -1142-4·(-1)·8650
Δ = 47596
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{47596}=\sqrt{4*11899}=\sqrt{4}*\sqrt{11899}=2\sqrt{11899}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-2\sqrt{11899}}{2*-1}=\frac{114-2\sqrt{11899}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+2\sqrt{11899}}{2*-1}=\frac{114+2\sqrt{11899}}{-2} $
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