X+4/x+3=11

Solution for X+4/x+3=11 equation:

X+4/X+3=11

We move all terms to the left:

X+4/X+3-(11)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

X+4/X-8=0

We multiply all the terms by the denominator


X*X-8*X+4=0

We add all the numbers together, and all the variables

-8X+X*X+4=0

Wy multiply elements

X^2-8X+4=0

a = 1; b = -8; c = +4;
Δ = b2-4ac
Δ = -82-4·1·4
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{3}}{2*1}=\frac{8-4\sqrt{3}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{3}}{2*1}=\frac{8+4\sqrt{3}}{2}
$