8650=x(114-0.055x)

Solution for 8650=x(114-0.055x) equation:

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:

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)


We get rid of parentheses

-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}
$