.2=X^2/55-x

Solution for .2=X^2/55-x equation:

.2=X^2/55-X

We move all terms to the left:

.2-(X^2/55-X)=0


Domain of the equation: 55-X)!=0

We move all terms containing X to the left, all other terms to the right

-X)!=-55

X!=-55/1

X!=-55

X∈R


We add all the numbers together, and all the variables

-(X^2/55-X)+0.2=0

We get rid of parentheses

-X^2/55+X+0.2=0

We multiply all the terms by the denominator


-X^2+X*55+(0.2)*55=0

We add all the numbers together, and all the variables

-1X^2+X*55+11=0

Wy multiply elements

-1X^2+55X+11=0

a = -1; b = 55; c = +11;
Δ = b2-4ac
Δ = 552-4·(-1)·11
Δ = 3069
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:

$\sqrt{\Delta}=\sqrt{3069}=\sqrt{9*341}=\sqrt{9}*\sqrt{341}=3\sqrt{341}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-3\sqrt{341}}{2*-1}=\frac{-55-3\sqrt{341}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+3\sqrt{341}}{2*-1}=\frac{-55+3\sqrt{341}}{-2}
$