X=1/11y-5

Solution for X=1/11y-5 equation:

X=1/11X-5

We move all terms to the left:

X-(1/11X-5)=0


Domain of the equation: 11X-5)!=0

X∈R


We get rid of parentheses

X-1/11X+5=0

We multiply all the terms by the denominator


X*11X+5*11X-1=0

Wy multiply elements

11X^2+55X-1=0

a = 11; b = 55; c = -1;
Δ = b2-4ac
Δ = 552-4·11·(-1)
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*11}=\frac{-55-3\sqrt{341}}{22}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+3\sqrt{341}}{2*11}=\frac{-55+3\sqrt{341}}{22}
$