X-3/x=7x/x+4

Solution for X-3/x=7x/x+4 equation:

X-3/X=7X/X+4

We move all terms to the left:

X-3/X-(7X/X+4)=0


Domain of the equation: X!=0

X∈R



Domain of the equation: X+4)!=0

X∈R


We get rid of parentheses

X-3/X-7X/X-4=0

We multiply all the terms by the denominator


X*X-7X-4*X-3=0

We add all the numbers together, and all the variables

-11X+X*X-3=0

Wy multiply elements

X^2-11X-3=0

a = 1; b = -11; c = -3;
Δ = b2-4ac
Δ = -112-4·1·(-3)
Δ = 133
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{133}}{2*1}=\frac{11-\sqrt{133}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{133}}{2*1}=\frac{11+\sqrt{133}}{2}
$