14x/(x^2+10)=2

Solution for 14x/(x^2+10)=2 equation:

14x/(x^2+10)=2

We move all terms to the left:

14x/(x^2+10)-(2)=0


Domain of the equation: (x^2+10)!=0

We move all terms containing x to the left, all other terms to the right

x^2!=-10

x^2!=-10/

x^2!=√-1/0

x!=NAN

x∈R


We multiply all the terms by the denominator


14x-2*(x^2+10)=0

We multiply parentheses

-2x^2+14x-20=0

a = -2; b = 14; c = -20;
Δ = b2-4ac
Δ = 142-4·(-2)·(-20)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-6}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+6}{2*-2}=\frac{-8}{-4}
=+2
$