(X)-(8/11x-5)=41

Solution for (X)-(8/11x-5)=41 equation:

(X)-(8/11X-5)=41

We move all terms to the left:

(X)-(8/11X-5)-(41)=0


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

X∈R


We get rid of parentheses

X-8/11X+5-41=0

We multiply all the terms by the denominator


X*11X+5*11X-41*11X-8=0

Wy multiply elements

11X^2+55X-451X-8=0

We add all the numbers together, and all the variables

11X^2-396X-8=0

a = 11; b = -396; c = -8;
Δ = b2-4ac
Δ = -3962-4·11·(-8)
Δ = 157168
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:

$\sqrt{\Delta}=\sqrt{157168}=\sqrt{16*9823}=\sqrt{16}*\sqrt{9823}=4\sqrt{9823}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-396)-4\sqrt{9823}}{2*11}=\frac{396-4\sqrt{9823}}{22}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-396)+4\sqrt{9823}}{2*11}=\frac{396+4\sqrt{9823}}{22}
$