(x^2+5)/7x=3

Solution for (x^2+5)/7x=3 equation:

(x^2+5)/7x=3

We move all terms to the left:

(x^2+5)/7x-(3)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We multiply all the terms by the denominator


(x^2+5)-3*7x=0

Wy multiply elements

(x^2+5)-21x=0

We get rid of parentheses

x^2-21x+5=0

a = 1; b = -21; c = +5;
Δ = b2-4ac
Δ = -212-4·1·5
Δ = 421
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{-(-21)-\sqrt{421}}{2*1}=\frac{21-\sqrt{421}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{421}}{2*1}=\frac{21+\sqrt{421}}{2}
$